two 16.0 $kg$ ice sleds are placed a short distance apart, one directly behind the other, as shown in the figure. a 3.11 $kg$ cat, initially standing on sled 1, jumps across to sled 2 and then jumps back to sled 1. both jumps are made at a horizontal speed of 2.00 $m/s$ relative to the ice. what is the final speed of sled 2? (assume the ice is frictionless.)
The final speed of sled 2 = 0.77 m/s
What is impulse?Impulse is the integral of the force (F) over the time interval (t) for which the force acts. Since force is a vector quantity, momentum is also a vector quantity. Momentum applied to an object produces a vector change equivalent to its linear momentum, and the resulting direction is also changed.
For the given case:
After first jump speed of sled 1 is = u₁
Since there is no external force acting on the sled-cat system there'll be no change in momentum.
u₁ × 16 + 2 × 3.11 = 0
u₁ = -0.38 m/s
Now, for sled 2
2 × 3.11 = (3.11 + 16)u₂
u₂ = 0.32 m/s
After the second jump:
-2 × 3.11 + 16 × v₂ = 0.32 × (16 + 3.11)
v₂ = 0.77 m/s
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How much energy is stored in the 180-µF capacitor of a camera flash unit charged to 300.0 V?
Energy is stored in the 180-µF capacitor of a camera flash unit charged to 300.0 V is 8.10 J.
A capacitor is a tool that stores electrical electricity in an electric-powered field by way of the distinctive feature of accumulating electric expenses on two close surfaces insulated from each other. it's miles a passive digital component with terminals.
The impact of a capacitor is called capacitance. A capacitor is an electrical component that shops capacity power. Capacitors hold wonderful and bad electricity on separate plates separated by way of an insulator. A capacitor(s) is called cap(s) for brief.
Calculation:-
energy stored in capacitor = C V^2 /2
= 180 x 10^-6 x 300^2 / 2 = 8.10 J
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a 500-w device is connected to a 120-v ac power source. what is the peak voltage across this device? a) 4.2 v b) 5.9 v c) 120 v d) 150 a e) 170 v
The peak voltage across this device would be 170v (rounded). So the answer is E.
What is peak voltage?It is the highest point or highest value of voltage for any voltage waveform. It is a power quality issue that occurs when devices that use Pulse Width Modulation, such as a variable frequency drive, is added to a power system. The resulting peak voltage is a result of the switching speed and length of cable (increasing impedance).
Now, we need to find the peak voltage based on the information given from the question.
Vrms = 120V (given)
the formula is Vrms = Vpeak / [tex]\sqrt{2}[/tex]
Vpeak = [tex]\sqrt{2[/tex]Vrms
= [tex]\sqrt{2}[/tex] * 120
Vpeak = 170v (rounded)
So, the peak voltage of this device would be (E) 170v.
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what is the wavelength (in pm) of an electron with a mass of 9.11 x 10-31 kg and a velocity of 2.963 x 106 m/s aleks
The wavelength of an electron is 215.5nm.
The de Broglie wavelength is calculated in what way?A description of the de Broglie wavelength is as follows:
The formula for wavelength is = h/mv, where h stands for Planck's constant, m for mass, and v for velocity.
The equation p = h/λ, where h is the Planck constant and is the wavelength, expresses the De Broglie relation, which states that there is a correlation between an electron's wavelength and momentum.
The wavelength of a wave is the distance between its two subsequent crests or troughs.
h = 6.62607015 × 10⁻³⁴ joule second.
m =9.11 x 10 ⁻³¹Kg
v = 2.963 x 10⁶m/s
λ = h / ( mv)
λ = 6.62607015 × 10⁻³⁴/9.11 x 10 ⁻³¹×2.963 x 10⁶
λ = 2.155×10⁻⁷
λ = 215.5nm.
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If the man pulls the sled with a 10 N
force, what is the horizontal component
of force? Refer to chapter 4, mechanics if
you do not remember how to resolve a
force into its components.
Answer:
Explanation:
The horizontal component of force is Fcosθ if the man pulls the sled with a 10 N force. Force has both a magnitude and a direction since it is a vector quantity.
What is force?A force is an external cause that, when applied, alters or has the potential to alter a body's condition. The body comes to rest while it is moving, and it moves when it is at rest.
The body's orientation, form, size, etc. may also alter as a result. An illustration would be to push or forcefully shove a door. Force has both a magnitude and a direction since it is a vector quantity. If the man pulls the sled with a 10 N force then the horizontal component of force is Fcosθ. Your training at this level should place a major emphasis on the idea that a push or even a pull was referred to as an force.
Therefore, the horizontal component of force is Fcosθ if If the man pulls the sled with a 10 N force.
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a satellite moves on a circular earth orbit that has a radius of 6.7 x 106 m. a model airplane is flying on a 15-m guideline in a horizaontal circle. the guideline is parallel to the ground. find the speed of the plane such that the plane and the satellite have the same centripetal acceleration.
The speed of the plane will have a factor of 0.668 with the satellite speed at the same centripetal acceleration.
We need to know about centripetal acceleration to solve this problem. The centripetal acceleration depends on the angular velocity and the radius. It can be written as
a = v² / R
where a is centripetal acceleration, v is velocity and R is radius.
From the question above, the given parameters are
R1 = 6.7 x 10⁶ m
R2 = 15 m
a1 = a2
By substituting the given parameters, we can calculate the speed of plane
a1 = a2
v1² / R1 = v2² / R2
v2² / v1² = R1 / R2
v2² / v1² = 6.7 x 10⁶ / 15
v2² / v1² = 6.7 x 10⁶ / 15
v2/v1 = 0.668
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when the core of a star reaches a temperature of about 100 million degrees (k), something new happens in the core. what is this new event?
When the core of a star reaches a temperature of about 100 million degrees (k), the new event named triple-alpha process happens where the helium will begin to fuse into carbon.
What is triple alpha process?The triple-alpha mechanism, which turns three helium nuclei into one carbon atom, will start to fuse helium into carbon when the temperature in the core reaches roughly 100 million degrees. There is a lot of heat produced by this.
The triple-alpha process is unusually sensitive to temperature; when the reaction's temperature is doubled, it proceeds nearly a trillion times faster! Therefore, while the fusing helium heats the core, which cannot expand to cool down, the increasing temperature prompts the helium fusion to abruptly proceed millions of times faster, which very quickly heats the core even more, which in turn prompts the helium to fuse way, way faster.
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a dockworker loading crates on a ship finds that a 29-kg crate, initially at rest on a horizontal surface, requires a 71-n horizontal force to set it in motion. however, after the crate is in motion, a horizontal force of 50 n is required to keep it moving with a constant speed. find the coefficients of static and kinetic friction between crate and floor.
The coefficients of static and kinetic friction between crate and floor are
0.25 and 0.176 respectively.
When a body is at rest and if a force is applied to move it, then it would require the force which is equal to the static friction force, if
fs is the static frictional force and the us is the static friction coefficient and Fn is the normal force
[tex]f_{s}[/tex] = us*Fn
Fn = mg
putting the appropriate values, we get
= 71/(29*9.8) = 71/284.2
= 0.2498 = 0.25
Now, similarly when body is in motion, kinetic frictional force is applied, so we can write
[tex]f_{k}[/tex] = uk*Fn
so putting the appropriate values, we get
= 50/mg = 50/284.2 = 0.1759
= 0.176
Hence the value of coefficient of static friction is 0.25 and the value of coefficient of kinetic friction is 0.176.
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a playground merry-go-round has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.350 rev/s. what is its angular velocity (in rev/s) after a 15.0 kg child gets onto it by grabbing its outer edge? the child is initially at rest.
Angular velocity (in rev/s) after a 15.0 kg child gets onto it by grabbing its outer edge is 1.575 rad/s.
The angular velocity of the merry-go-round after a child gets on it is equal to the angular velocity of the child plus the angular velocity of the merry-go-round.
The angular velocity of a rotating object can be calculated using a formula:
ω = ω + (m/r)
where ω is the original angular velocity, m is the mass of an object that's been added to it, r is its radius, and (m/r) is the change in mass divided by its radius. When we plug in our values for this problem, we get:
ω = 0.350 rad/s + ((15 kg)/(1.8 m)) rad/s
= 0.350 rad/s + 1.25 rad/s
= 1.575 rad/s
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a bear sling is used in some national parks for placing backpackers' food out of the reach of bears. as the backpacker raises the pack by pulling down on the rope, the force f needed:
Force is to be known for this problem.
What is force?
In physics, force is the push or pull that an object feels when its mass causes it to change its velocity. An external force has the ability to change a body's resting or moving state. It moves and has a size.
What constitutes speed?
the speed at which the position of an object is shifting, in any direction. Speed is defined as the product of the distance traveled and the time needed to cover that distance. Since speed simply has a focus and no magnitude, it is a scalar number.
2T cos∅ =μg
⇒ if weight (μg)
rises
⇒∅ increases
⇒ cos∅ decreases
⇒T increases
⇒F will also increases
But ∴ Cos 90° = u
⇒ not possible.
Therefore, the force is to be needed.
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A skier (m = 100 kg) is on level ground with a coefficient of kinetic friction of 0.05 m
moving at a speed of 100m/s. Calculate the distance the skier will go before they stop.
Use conservation of energy.
The distance the skier will go before they stop is 10193.68m.
Given ; Mass =100kg
coefficient of kinetic friction μ=0.05m
u=100m/s
v=0
μg=a
a= μg=0.05 x 9.81=0.4905 m/s²
v²-u²=2as
[v²-u²]/2a= s
-100²/2(0.4905)
s=10193.68m (neglecting the negative sign)
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Vector A is 3.2 m in length and points along the positive y-axis. Vector B is 4.6 m in length and points
along a direction 195° counterclockwise from the positive x-axis. What is the magnitude of the resultant
when vectors A and B are added?
the earth exerts a gravitational force on a person standing on the surface. the person also exerts a gravitational force on the earth. based on newton's laws, how do these two forces compare?
Answer:
F = M a Newton's Second Law
The person is undergoing no acceleration, thus the upwards force of the earth on the person exactly balances the attraction of the earth on the person's center of gravity
(Also, Newton's third law that for every action there is an opposite and equal reaction}
A gas receives from an external thermal source an amount of heat equal to 1000 J. This energy, in addition to producing heating in the gas, causes its expansion, with the consequent performance of work equivalent to 600 J. What was the change in the internal energy of the gas? gas?
help someone help me
Hello..!
Subject: ThermodynamicsThe first law of thermodynamics relates work and transferred heat exchanged in a system through a new thermodynamic variable, internal energy. This energy is neither created nor destroyed, only transformed.
We can think of gas as a thermodynamic system, all because gases can work and absorb heat, and then they can turn all that into energy.
The formula for the change in energy is given by the first law of thermodynamics expressed as:
[tex] \: \: \: \: \: \: \: \: \: \: {\boxed{\boxed{ \sf\large \rm \Delta U = Q - W }}}[/tex]
Being:
ΔU = change in energyQ = added heatW = Work doneProblem:
A gas receives from an external thermal source an amount of heat equal to 1000 J. This energy, in addition to producing heating in the gas, causes its expansion, with consequent performance of work equivalent to 600 J. What was the change in the internal energy of the gas? gas?
Data:
ΔU = ¿? (Meet)Q = 1000 JW = 600 JNow adding the data in the formula to find the energy change:
[tex] \sf\large \rm \Delta U = 1000J - 600J[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{\boxed{\boxed{\large \rm \Delta U = 400 J}}}[/tex]
[tex]\begin{gathered}\rule{7cm}{0.01mm}\\\texttt{Good studies! :D}\\\rule{7cm}{0.01mm}\end{gathered}[/tex]
A 5 kg block is pulled across the ground to the right by a tension force of 40 N with a frictional force of 8 N opposing the motion. What is the acceleration of the object?
The Acceleration of the object = 6.4 m/s²
Mass of block (m) = 5 kg
Action force on block, (F₁) = 40 N
Frictional force opposing the motion (F₂) = 8 N
Acceleration of the object (a) = ?
⇒ Net force = Action force on block - Opposing friction force
⇒ F = F₁ - F₂
⇒ F = 40 - 8
⇒ F = 32 N
Net force of the block (F) = 32 N
Mass of block (m) = 5 kg
F is the Force in N.
m is the Mass in kg.
a is the Acceleration in m/s².
F = ma
⇛ a = F/m
⇛ a = 32/5
⇛ a = 6.4 m/s²
a golf ball of mass 45.93 g has a velocity of 74.22 m/s immediately after being struck. if the club and ball were have an average contact force of 8896 n, how long does the contact last?
The time for that contact force is 0.00038 s.
An impulse is a surprising pressure or choice — this will be an electrical impulse or an impulse to get a few pizzas. if you act on an unexpected feeling or concept, you're following an impulse. it's like a whim: an impulse is not something you have given quite a few concepts. The impulse of pressure is the product of the resultant pressure ΣF and the length of this force Δt if the pressure is constant. The impulse of pressure is the purpose of changes to movement and consequently changes to momentum.
Momentum is a vector amount that has an equal path to the velocity of the item. the amount of force accelerated by the time it's far implemented is called impulse. Impulse is a vector quantity that has an equal path to the pressure. Momentum and impulse have equal gadgets: kg·m/s
Calculation:-
mass = 45.93 g = 0.046 kg
velocity = 74.22 m/s
Impulse = Change in Momentum
Ft = mv
t = 0.046 × 74.22 / 8896
= 6455.696 N
= 3.8 × 10⁻⁴ Sec
Therefore, the time for that contact force is 0.00038 s.
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a car traveling with a constant velocity quickly comes to rest. while slowing down, the passengers inside the car are pushed forward by the force of .
Using the concepts of motion, we got that Ma is the force exerted on the passengers inside the car when a car traveling with a constant velocity quickly comes to rest.
We know very well that according to newton second law of motion,
if a moving object is moving with some velocity v at any particular time t, then there is force acting on that object and that force is given by
F= dp /dt,
where dp is defines as change in momentum of the object. In other words,
dp=M×([tex]v_f_i_n_a_l[/tex] - [tex]v_i_n_i_t_i_a_l[/tex])
where [tex]v_f_i_n_a_l[/tex] and v[tex]_i_n_i_t_i_a_l[/tex] are the velocities of the object in different time.
So suppose car has some mass M kg
It is given that final velocity of the object is =0 as the car comes to rest,
suppose initial velocity is v
Therefore, F=[M×(0-v)]/t
=> F= -M×(v/t)
=> F= -Ma because acceleration =velocity/time
Here negative sign shows that force acts on the person in opposite direction of frictional force applied by the road.
Hence, when a car traveling with a constant velocity quickly comes to rest. while slowing down, the passengers inside the car are pushed forward by the force - Ma.
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A 0. 25-kg toy car experiences a net force of 9. 0 n while slowing down to a complete stop. What is the magnitude of its acceleration?.
Answer:
a = 36 m/s
Explanation:
Given:
F = 9 N
m = 0.25 kg
a= ?
Use the equation:
F = ma (divide by m on both sides to get a alone)
a = F/m= 9/0.25 = 36 m/s
a ball is kicked with an initial velocity of 23 m/s in the horizontal direction and 14 m/s in the vertical direction. (assume the ball is kicked from the ground. for each answer, enter a number.) (a) at what speed (in m/s) does the ball hit the ground? m/s (b) for how long (in s) does the ball remain in the air? s (c) what maximum height (in m) is attained by the ball?
The speed of the ball is 192m/s. The long of the ball is 2.85s.The height of the ball is 2.13m.
How to calculate speed?A)The speeds at these points are equal since the starting position and the point at which it touches the ground have the same elevation. Solving the product of the horizontal and vertical velocities yields the final speed. Which is
vf=√(V[tex]ox[/tex])²+(V[tex]oy[/tex])²
vf=√(23m/s)²+(14m/s)²
vf=192m/s
How to calculate long?B)Take into account the starting point and the highest point, respectively.
We are aware that the vertical velocity is zero at the highest point. Additionally, we are aware that the duration of the flight from start to finish is twice as long.
So, we'll apply the formula t=v[tex]f[/tex]-v[tex]o[/tex]/a
t=2(v[tex]top[/tex]-v[tex]o[/tex])/a
t=2(0m/s-14m/s)/-9.81m/s
t=2.85s
How to calculate height?C)Using the formula, the highest height that can be reached can be determined.(v[tex]f[/tex])²=(v[tex]0[/tex])²+2ay
This is how the maximum height is determined:
(v[tex]f)[/tex]²=(v[tex]0)[/tex]²+2ay
y[tex]max[/tex]=(v[tex]top[/tex])²-(v[tex]o[/tex])²÷2a
y[tex]max[/tex]=(0m/s)²-(14m/s)²÷2(-9.81m/s)²
=2.13m
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Where do you predict the energy that is not transferred into the electrical grid is lost as it moves from
system to system?
The energy that is not transferred into the electrical grid is lost as heat as it moves from system to system.
The electricity that is produced in power stations reach the consumers through a complex system of electric cables and grid. The grid usually means transformers which is used to step up and step down the voltage when necessary.
The first transformer from the power plant steps up the voltage of the current for the purpose of long distance transmissions. Before entering the household another transformer steps down the voltage to avoid short circuiting the electrical appliances. During all these processes the current is carried through electrical lines. Due to its contact with the atmosphere some energy is lost has heat in the air.
Therefore, the energy that is not transferred into the electrical grid is lost as heat as it moves from system to system.
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the distance between x-ray tube and the bucky (the area that stores the film), is referred to as the .
An x-ray cassette is kept in a device called a "bucky" that resembles a drawer. It can be installed either on the wall or underneath the exam table.
These days, buckys have an internal grid that absorbs dispersed radiation to enhance the clarity of x-ray images. The oscillating option that modern buckys have added further aids in preventing scattered radiation from reaching the x-ray cassette and increases the quality of the x-ray image.To ensure that a high-quality x-ray image is created when using Bucky, an increase in radiation exposure parameters (kVp and mAs) is necessary. If Bucky is not utilized, the same x-ray technique can be carried out with lower exposure factors, but the image quality will suffer.To know more about x-ray
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A 0. 0850-kg arrow is fired horizontally. If the bowstring exerts an average force of 89. 0 n on the arrow over a distance of 0. 782 m, with what speed does the arrow leave the bow?.
40.47 m/s is the speed at which the arrow departs the bow.
Does velocity not depend on gravity?
An object's horizontal velocity is constant for small displacements and operates independently of the vertical force of gravity. The horizontal and vertical halves of an object that is projected at an angle to gravity can also be separated. The force of gravity has no impact on the horizontal velocity component either.
The arrow will start moving and accelerating as soon as it is let go from the bow. The arrow obeys the second law of motion, according to Newton. The method
m = mass of the arrow (kg) = 0.0850 kg
a = acceleration of the arrow (m/s²)
F = force (N) = 89.0 N
F=m*a
a = 1,047.059 m/s²
When an object accelerates, it will travel in a non-uniform manner. The method
[tex]v^{2} = v_{0} ^{2} +2*a*d[/tex]
= 40.47 m/s
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An astronaut orbits the Earth in a space station.Which is a vector quantity
The force of gravity is the only force acting upon their body. The astronauts are in free-fall.
If the astronaut is formed of the same amount of material as before, the mass will always be the same.
So, when asked what the astronauts' mass is on the space station, we can respond it's still 65 kg. Because there is no gravity in space, astronauts float around.
Everyone understands that the gravitational force decreases with distance from Earth. Astronauts are so far away from Earth that gravity is negligible. This is why NASA refers to it as microgravity.
Mass is the same whether measured on Earth or on the International Space Station. Weight can vary based on gravitational pull, such as on the Moon, where weight is one-sixth that of Earth.
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what is the magnification of an astronomical telescope whose objective lens has a focal length of 79 cm and whose eyepiece has a focal length of 2.9 cm ? follow the sign conventions.
The magnification of an astronomical telescope is -27.24 .
The magnification of a telescope is actually a relationship between two independent optical systems: the telescope itself and the eyepiece that is being used.
To determine the power, divide the focal length of the telescope (in mm) by the focal length of the eyepiece (in mm)Magnification is denoted by MMathematically it is M = -(T/E)Focal length of the telescope = T = 79 cm = 790mm
Focal length of the eyepiece = E = 2.9 cm = 29mm
M = -[tex]\frac{T}{E}[/tex]
M = -[tex]\frac{79}{2.9}[/tex]
M = -27.24
Therefore, the magnification of an astronomical telescope is -27.24.
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An aeroplane lands on a runway at a speed of 180 km/hr and is brought uniformly in 30 seconds.what distance does it covers on the run way before coming to rest
This can be calculated by using motion equations, The distance covered on the runway before coming to rest
Initial speed is 180 km/hr = 50 m/s
time took to come to rest is = 30 sec
so we can write, here we are assuming that there is no frictional force is applied externally or internally to the system.
u = 50 m/s
v = 0 m/s
t = 30 s
we know that distance travelled = x
so, x =
putting the appropriate values, we get that
x = [tex](\frac{50+0}{2} ) 30[/tex]
x = 750 m
Hence the distance travelled before coming to rest is 750 m.
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Jasper is using an equal force to move a tennis ball and a bowling ball. What prediction can Jasper make about the force and the motion of the objects?
Both objects will have an equal change in motion.
Neither object will have any change in motion.
The bowling ball will have a greater change in motion.
The tennis ball will have a greater change in motion.
When Jasper uses the same amount of force to move a tennis ball and a bowling ball, d)the tennis ball will have a greater change in motion.
What is the second law of motion of Newton?Newton's second law states that an object's net force is equal to the sum of its mass and acceleration.
F = ma is the formula, where F denotes force, m denotes mass, and a denotes acceleration.
When the force F is constant and we rearrange the equation, we get acceleration as a = F/m. We know that acceleration is inversely linked to the mass m. Greater mass results in smaller acceleration, and conversely, smaller mass results in greater acceleration.
We know that mass of bowling ball is more than tennis ball.
Tennis ball > bowling ball will have the highest rate of acceleration since the relationship between acceleration and mass is inverse.
It follows that tennis balls will accelerate their change of direction more quickly than bowling balls.
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a bus traveled 387 km in 5 h.one hour of the trip was in city traffic. the bus's city speed was just half of its speed on open highway. the rest of the trip was on open highway. find the bus'scity speed
The bus'scity speed is 77.4km/hr.
How is speed defined in?What constitutes speed? the speed of a change in an object's position in any direction.
Speed is the rate of change in location of an item, expressed in meters per second. If something starts at the origin and goes three meters in three seconds, for instance, its speed is one meter per second. Like distance divided by time, the equation for speed is straightforward.
A change in an object's position over time is referred to as motion in physics. Displacement, distance, velocity, acceleration, time, and speed all play a role in how motion is defined. Speed is a scalar variable that describes how quickly an object travels through space with regard to time.
speed = distance/time
speed =387/5
speed =77.4km/hr.
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Gabriel kicks a soccer ball so that it has an initial velocity 22 meters per second, at an angle of 16 above the ground. How much time does it take for the soccer ball to reach its maximum height?
0.62s
2.24s
0.77s
2.16s
WHICH ONE???
The time taken to reach the maximum height, given that the ball has an initial velocity of 22 m/s is 0.62 s
How do I determine the time taken to reach the maximum height?The time taken to reach the maximum height can be obtained by using the following formula:
t = uSineθ / g
Where
t is the time taken to reach the maximumu is the initial velocityθ is the angle of projectiong is the acceleration due to gravityNow, we shall determine the time taken to reach the maximum as follow:
Initial velocity (u) = 22 m/sAngle of projection (θ) = 16 °Acceleration due to gravity (g) = 9.8 m/s²Time taken to reach the maximum height (t) = ?t = uSineθ / g
t = (22 × Sine 16) / 9.8
t = 0.62 s
Thus, the time taken is 0.62 s
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What is the Period (T) of this wave?
a. 3.9 cm
b. 0.4 Hz
c. 2.5 sec
d. 1.6 cm/s
The time period of the wave is 2.5 seconds. Option C
How is the duration of a wave defined?
The duration of time it takes for two crests of a single wavelength to pass a specific location is termed as the time period of a wave.Seconds are frequently used to describe the wave period.Since frequency and wave period are inversely proportional, the wave period can be calculated using the following formula:
T = 1/f
T = λ /v
where T is the time period in seconds, f is the wave frequency, is the wavelength in meters, and v is the speed in meters per second.
Time is divided into periods by the quantity of oscillations. Two oscillations are shown in the diagram. By counting the wave's crests one by one starting at the 0s point, this may be seen. Two oscillations end in five seconds. 2 divided by 5 equals 2.5 seconds.
Hence, Option c) 2.5 is correct.
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A 2.5 newton weight falls freely from rest from the roof of a building. What is the total distance the weight falls in the first 4.0 seconds?
Answer:
Explanation:
L = g·t² / 2 = 9.8·4.0² / 2 = 78.4 m