A figure skater begins spinning counter-
clockwise at an angular speed of 3.2 pi rad/s.
During a 4.6 s interval, she slowly pulls her
arms inward and finally spins at 7.7 pi rad/s.
What is her
average angular acceleration
during this time interval?
Answer in units of rad/s?.

The angular velocity is infinity.

it's not possible to calculate the kinetic energy change when the angular velocity becomes infinity, it's an abstract concept.

PART 1

The angular velocity of an object is given by the formula:

ω = v/r

where

v is the linear velocity and

r is the distance from the axis of rotation.

The man's initial angular velocity is:

ω = (0.37 rev/s) * (2π rad/rev)

= 2.34 rad/s

As the man moves closer to the center, his distance from the axis of rotation decreases, so his angular velocity will increase.

To find the new angular velocity, we can use the same formula:

ω = v/r

since the radius decreases to 0, the angular velocity becomes infinity.

PART 2

The change in kinetic energy is given by the formula:

ΔK = 1/2 * I * (ω_f^2 - ω_i^2)

where

For a solid cylinder, the moment of inertia is:

I = (1/2) * m * r^2

where

The moment of inertia for the merry-go-round is:

I = (1/2) * (29 kg) * (1.2 m)^2

= 15.12 kg * m^2

The change in kinetic energy can be calculated as:

ΔK = 1/2 * (15.12 kg * m^2) * (∞^2 - (2.34 rad/s)^2)

= infinity J

Note that it's not possible to calculate the kinetic energy change when the angular velocity becomes infinity, it's an abstract concept.

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The body will be at a temperature of 60°F after around 72 minutes.

The problem can be solved using Newton's law of cooling, which states that the rate of change of temperature of an object is proportional to the difference in temperature between the object and its surroundings. Mathematically, this can be represented as:

T(t) = T_s + (T₀ - T_s) e^(-kt)

where T(t) is the temperature of the object after time t, T₀ is the initial temperature of the object, T_s is the temperature of the surroundings, t is time and k is a constant of proportionality called the cooling coefficient.

Use the initial condition T = 90°F at t = 10 min, T_s = 50°F, T₀ = 100°F to solve for the value of k.

T(t) = T_s + (T₀ - T_s) e^(-kt)

90°F = 50°F + (100°F - 50°F) e^(-k)(10)

40°F = 50°F e^(-k)(10)

e^-10k = 0.8

k = 0.0223

thus we can calculate the time it takes for the body to reach a temperature of 60°F:

T(t) = T_s + (T₀ - T_s) e^(-kt)

60°F = 50°F + (100°F - 50°F) e^(-0.0223)(t)

10°F = 50°F e^(-0.0223)(t)

e^(-0.0223)(t) = 0.2

t = 72.1721

t ≅ 72 minutes

Therefore, it would take around 72 minutes for the body to reach a temperature of 60*F.

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The average speed of that person with two constant speed for a certain distance is 4 m/s.

Assume the distance from point a and b is c, As per data given velocity from a to b = 5.10 m/sec. So,

time a to b = c : 5.10.

Since the constant speed is 3.3. then

time b to a = c : 3.30

The we can determine the average speed as follow:

Total distance = c + c = 2c

Total time = time a to b + time b to a

Total time = c : 5.10 + c : 3.30

Total time = 0.196c + 0.303c

Total time = 0.499c

Average speed = total distance : total time

Average speed =  2c : 0.499c

Average speed = 4.00801603206

Let round the result, so the average speed = 4 m/s

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The kinetic friction observed by skier when he starts from rest on the higher peak is 0.0.0313.

Here is the information we need:

h1 denotes the starting height (850 m)

The final height is given by h2 (750 m)

is the inclination angle (30°)

k is the kinetic friction coefficient.

The total distance traveled is given by d.

The distance traveled downward is denoted by d1.

The distance traveled uphill is denoted by d2.

Where:

d=d1 + d2 =h1/sin + h2/sin =850/sin30+750/sin30

=3200 m

Because the skier begins and ends at rest, the change in kinetic energy is zero.

When traversing a distance d, the energy dissipated by kinetic friction (negative sign) is equal to the change in gravitational potential energy.

[h2-h1]k =h1-h2d

=850-750/3200

=0.0313

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Complete question : Two snow-covered peaks are at elevations of 850 and 750 m above the valley between them. Both elevations have an incline of 30 degrees. A ski-run extends from the top of the higher peak to the top of the lower one. A skier starts from rest on the higher peak and stops on top of the lower peak. What is the kinetic friction coefficient?

A falling item with a mass of 4 kg is 3 metres above the earth and is travelling at a speed of 7 m/s at that precise time. The item has a mechanical energy of 216.4 Joules.

A falling object's kinetic energy (KE) and potential energy may be used to compute its mechanical energy (PE).

KE = 1/2 mv ²

= 1/2 X 4 X 14 = 98

where m is the item's mass and v is its velocity,

The equation PE = m * g * h gives the potential energy of an item.

PE =  4 X 9.8X 3 =  117.6

E = KE + PE gives the object's total mechanical energy.

E = 98 + 117.6

= 215.6 J

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The speed of the roller coaster at point E is 40 m/s.

The speed of the roller coaster at point F is 49 m/s.

The speed of the roller coaster at point E is calculated by applying the following formula as shown below.

v = √ ( 2gΔh )

where;

At point E, the change in height of the coaster, Δh  = 120 m - 40 m = 80 m

v = √ ( 2gΔh )

v = √ ( 2 x 10 x 80 )

v = 40 m/s

At point F, the change in height of the coaster, Δh  = 120 m - 0 m = 120 m

v = √ ( 2gΔh )

v = √ ( 2 x 10 x 120 )

V = 49 m/s

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The highest frequency audible is the 24th harmonic. The fact that a standing wave on a wire generates an identical sound wave in the air is used in component (b).

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Acceleration (a) is the change in velocity (Δv) versus the change in time (Δt), given by the formula a = Δv/Δt. This allows you to measure how quickly the velocity changes in meters per second (m/s^2). Acceleration is also a vector quantity, so it contains both magnitude and direction. Negative acceleration is termed as deceleration

Deceleration can be calculated by dividing the final velocity minus the initial velocity by the time it takes for this velocity to drop.

The known and unknown quantities from the question are as follows:

u = initial velocity = ? m/s

v = final velocity = 160 m/s

a = acceleration = -0.5 m/s²

t = time interval = 8 min × 60 s/1 min = 480 s

Calculate the initial velocity using the following kinematic equation.

v = u + at

Solve for u.

u = v - at

u = 160 m/s - (-0.5 m/s² × 480 s) = 400 m/s

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The weight of the truck is approximately 254,979 N or 254.9 kN

To find the weight of the truck, we can use the principle of buoyancy, which states that the buoyant force exerted on an object submerged in a fluid is equal to the weight of the fluid that is displaced by the object.

First, we need to find the volume of the water displaced by the boat when the truck pulls onto it. We can use the dimensions of the boat and the amount it sinks in the water to calculate this. The boat is shaped like a brick, so we can assume it has the same dimensions on the top and bottom.

The boat's width is 7.7 m and its length is 6.2 m. The boat sinks 5.57 cm or 0.0557 m in the water.

The volume of the water displaced is the product of the boat's width, length, and the amount it sinks in the water.

Volume of water displaced = 7.7 m x 6.2 m x 0.0557 m = 25.9 m^3

Next, we can use the density of water, which is about 1000 kg/m^3 to find the weight of the water displaced.

Weight of water displaced = 1000 kg/m^3 x 25.9 m^3 = 25900 kg

Finally, we can use the weight of the water displaced to find the weight of the truck using the equation of buoyancy force which is equal to the weight of the fluid displaced.

Weight of truck = weight of water displaced x g

Weight of truck = 25900 kg x 9.81 m/s^2 = 254979 N

Therefore, the weight of the truck is approximately 254,979 N or approximately 254.9 kN.

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A metal ball bearing that has a 41.3 mm circumference weights 8.77 g. the metal has a density of 7.816 g/cm3. The mass of a material per unit of volume is its density.

We must first estimate the volume of the metal ball bearing before dividing the mass by the volume to obtain the density of the metal.

First  calculate the radius,

C = 2πr = 41.3mm = 4.13cm

here, we can find the radius,

r = c/2π = 4.13/2π = 0.65cm

to find the volume,

V = 4/3πr³

V = 4/3 π X 0.65³

V =  1.14cm³

now, to calculate density,

m = 8.77g

d = m/v

d = 8.77/1.14

d = 7.6 g/cm³

Finally, by dividing the mass by the volume, we get at the metal's density, which comes to around 7.6 g/cm3.

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The matte with is silver should be metallic, so it reflects light at all wavelengths, so that the infrared light returns to the body and decreases the radiation radiation emitted, thus keeping it warmer.

What is meant by radiation?

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The weight of a bear on earth that has a mass of 550 kg is found to be 5390 N.

A mass may be characterized as a type of dimensionless quantity that significantly represents the amount of matter in a particle or object. The standard unit of mass in the International System (SI) is the kilogram (kg).

According to the question,

The mass of a bear = 550 kg.

We have to calculate its weight,

The formula for calculating weight is as follows:

                    = 550 × 9.8 = 5390 N.

Therefore, the weight of a bear on earth that has a mass of 550 kg is found to be 5390 N.

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The FIT principles are a set of guidelines for designing effective exercise programs. They include:

Frequency: How often you perform the exercise. To improve flexibility, aim to stretch at least 2-3 times per week.

Intensity: How hard you work during the exercise. When stretching, intensity should be moderate and not painful.

Time: How long you perform the exercise. Hold each stretch for 15-30 seconds and repeat each stretch 2-4 times.

Type: The specific exercises you perform. Include a variety of stretches for different muscle groups, such as the hamstrings, quadriceps, and lower back.

By following these principles, you can create a stretching routine that is effective for improving your flexibility. It's important to keep in mind that flexibility is also depend on several factors such as age, injury history, and genetics.

So, it's always good to consult with a physical therapist or physician before starting any new exercise program.

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Some of the velocity from a collision between two vehicles crumples their bodies. A purposeful loss of kinetic energy occurs.

According to the rule of conservation of momentum, when two bodies contact in a closed or isolated system, their combined momentum before and after the collision must be identical if no outside force is acting on them. In other words, the system momentum is unchanged.

Momentum is defined as p = mv (in kg/s).

Where V is a body's speed, m = the body's mass, In order to maintain momentum

mv = unchanging

This is,

m1v1 = m2v2

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Height contours are used to indicate horizontal changes in altitude on a chart with a 500 millibar scale, which are equivalent to changes in pressure on the same horizontal axis.

The complete question is,

In order to depict horizontal changes in altitude that correlate to horizontal changes in pressure on a chart with a 500 millibar scale, ___ are used.

the isobars and the jet streams

d. height contours; c. isotachs.

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After the original electrodes 0.8nC are expanded until they are 20 cm in diameter.

What is meant by diameter?

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"A motion to dismiss should be filed if alienation of affection is not recognized as an issue that can be litigated in that state.

In physics, motion is defined as a change in a body's position or orientation over time. Translation is the term for motion along a line or a curve. Rotation is another motion that modifies a body's orientation.

The four types of motion are: linear, rotary reciprocating and oscillating.

Hence , If the state does not recognize alienation of affection as a matter that can be argued, a move to dismiss should be made.

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The question is incomplete, the complete question is:

"His state no longer recognizes alienation of affection as an issue that can be litigated. Which Motion should be filed ?

On a 480/277-volt system where the line-line-line fault current has been estimated to be 30,000 amperes, the approximate line-to-ground arcing fault value is 17,321 amperes.

The approximate line-to-ground arcing fault value for a 480/277-volt system is determined by calculating the line-line-line fault current and then dividing it by the square root of three (√3). The value of the line-line-line fault current must first be determined, which is 30,000 amperes in this case.

Next, the line-to-ground arcing fault current value is calculated by dividing the line-line-line fault current by the square root of three (√3), which is equal to 17,321 amperes. To arrive at this number, we use the following formula:

Line-to-ground arcing fault current = line-line-line fault current / √3

Therefore, the approximate line-to-ground arcing fault current value for a 480/277-volt system where the line-line-line fault current has been calculated to be 30,000 amperes is 17,321 amperes.

To summarize, the approximate line-to-ground arcing fault value for a 480/277-volt system is determined by calculating the line-line-line fault current, which is 30,000 amperes in this case, and then dividing it by the square root of three which is equal to 17,321 amperes. This is the approximate line-to-ground arcing fault current value that would be expected in such a system.

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The time required for the rock to reach the ground is 1.11 second.

Acceleration is rate of change of velocity with time. Due to having both direction and magnitude, it is a vector quantity. Si unit of acceleration is meter/second² (m/s²).

Initial height of the rock: h = 6.00 m.

Acceleration due to gravity: g = 9.8 m/s²

Let,  the time required for the rock to reach the ground is = t.

Then:

h = 1/2 × gt²

t = √(2h/g)

= √ {(2 × 6.00)/9.8} second.

= 1.11 second.

Hence, the time required for the rock to reach the ground is 1.11 second.

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Answer:

The black suv gets pushed and jumps the curb because of the momentum the silver sedan had during impact.

Explanation:

Because the silver sedan ran the light and hit the black suv at full speed, the momentum from the sedan will have enough force to push the black suv into the curb.

The density of the object (weighing 297 N in air is immersed in water after being tied to a string connected to a balance, the scale now reads 264 N immersed in oil, the object appears to weigh 272 N) is:

(1) The density of the object = 9,181.81 kg/m³

(2) The density of oil = 773.03 kg/m³

The buoyant force is the upward force that a fluid exerts on an object. Archimedes' Principle states that buoyant force equals the weight of the displaced fluid.

To determine the density of an object:

First, we'd calculate the buoyant force acting on the object using the formula:

Fb = Fa - Fw

Where,

Fb = buoyant force (N)

Fa = the weight of object in air (N)

Fw = the weight of object in water (N)

= 297 - 264

= 33 N

Now, determine the volume of the object:

V = Fb/ρg

= 33 / (1000) (9.8)

= 0.0033 m³

The mass of the object in air:

Ma = Fa/g

= 297 / 9.8

= 30.30 kg

Hence,

So, the density of the object:

ρ = m/v

= 30.30 / 0.0033

= 9,181.81 kg/m³

The buoyant force in oil:

Fb = Fa = Fo

= 297 - 272

= 25 N

ρ = fb/vg

= 25 / (0.0033 ) (9.8)

= 0.03234

= 773.03 kg/m³

So, the density in oil = 773.03 kg/m³

The question is incomplete, it should be:

An object weighing 297 N in air is immersed in water after being tied to a string connected to a balance. the scale now reads 264 N, immersed in oil, the object appears to weigh 272 N, find the density of the object. answer in units of kg/m3 .

Find the density of the object.

Answer in units of kg/m³

PART TWO

Find the density of the oil.

Answer in units of kg/m³

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Answer:

Weight

Explanation:

The magnitude of the gravitational force acting on an object is weight of the object.

Answer: Option B

Explanation:

Any kind of force is a vector quantity having magnitude and direction. And it is also known that all kinds of forces obey Newton’s second law of motion. This means that the magnitude of any kind of force will be equal to the product of mass and acceleration exhibited by the object.

As the term acceleration is also a vector quantity in the second law of motion, so the direction of acceleration will define the direction of force. Thus for the gravitational force, the acceleration will be acting downward and the acceleration of the object pulled due to gravitational force will have acceleration due to gravity.

So the Newton’s second law of motion representation of gravitational force will be

Now this product is also equal to the weight of the object as weight of any object is defined as the mass of the object influenced by gravitational pull.

The direction of the force on the charge at the origin is towards the charge at (0.53, 0.41) m, since the charges have opposite signs and attract each other.

The direction of the force exerted on a point charge at the origin by a second point charge can be found using Coulomb's law, which states that the force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them. The formula for the force is:

F = k * q1 * q2 / r^2

where k is the Coulomb constant (8.99 x 10^9 N * m^2 / C^2), q1 and

q2 are the charges, and

r is the distance between the charges.

To find the direction, we must first find the components of the force along the x and y axes.

Then, we can use arctan to find the angle relative to the positive x direction.

The distance between the charges can be found using the Pythagorean theorem:

[tex]r = \sqrt{((0.53 m)^2 + (0.41 m)^2)[/tex] = 0.65 m

The x and y components of the force can then be found using the formula:

Fx = F * cos(θ) = k * q1 * q2 * x / r^3

Fy = F * sin(θ) = k * q1 * q2 * y / r^3

where θ is the angle between the force and the positive x direction, and x and y are the x and y components of the displacement vector between the charges, respectively.

Finally, the direction of the force can be found using arctan:

θ = arctan(Fy / Fx)

The direction of the force on the charge at the origin is towards the charge at (0.53, 0.41) m,

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The body and through a specific angle experience angular accelerations of 0.87266 rad/sec2 and 12566.8 rad, respectively.

A rotating rigid body's angular velocity rises from 500 to 1500 rev/min under the given conditions.

Time= 120s

Finding - Angle and angular acceleration

The basic idea is that we must change rev/min to rad/sec.

ωf= ωi + αt

ωf- ωi = αt

Formula for angular acceleration: = [f- i]/t

Angle deviation formula: =it + t2/2

Calculations-

Rev/Min to rad/Sec conversion

I equals 500 rev/min

500 x 2 rad/rev x 1 minute and 60 seconds equals 52.3598 rad/sec.

f = 1500 rev/min

=1500 x 2 rad/rev x 1 minute and 60 seconds = 157.079 rad/sec

52.3598 rad/sec for I

ωf=157.079rad/sec

Now, to calculate angular acceleration, use the formula: [f- i]/t.

52.3598 rad/sec − 157.079 rad/sec = 120

1.872666 rad/sec

To calculate the angle deviated, enter -=i t + t2/2.

=52.3598 x 120 + [0.87266 x 120 x120]/2

ΔФ= 12566.8rad

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The point of the celestial sphere that is directly opposite the nadir and vertically above the observer is known as Zenith.

Perseus, auriga, taurus, gemini are zenith at sunset tonight. Stellarium is a open software that shows real time 3d sky images. From which you can know the position of stars, planets, constellations and other sky objects. If you are using stellarium mobile app, just point it towards the sky and it will show the celestial objects with names. The rising constellations rotate based on our Earth and where it is as it travels through space. It can be predicted through stellarium.  The time period zenith every so often approach the best factor, way, or stage reached with the aid of using a celestial frame on its every day obvious direction round a given factor of observation.

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The point in the sky or the celestial sphere that is immediately above the observer is called the zenith.

The point on the celestial sphere that is immediately above a viewer on Earth is called the zenith. The nadir is the point directly beneath you that is 180 degrees opposite the zenith. To see your sky, drag the "Markings" pane to the side. You can now figure out the limits of the constellations.

On the meridian, roughly in the middle of the "sky," is where the zenith is located the area of the sky directly overhead, altitude = 90 degrees. In more specific terms, it is situated where declination and observer latitude are equal. The celestial equator and the ecliptic are additional reference points on the planisphere.

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In the position time graph, between 4 and 6 seconds, the object is at rest because the change in position with time is zero.

A position - time graph is a type of graph in which the position of an object is plotted against time of motion of the object.

In a position time graph, the slope of the graph is the velocity of the object since velocity is defined as the change in displacement with change in time.

From the given position - time graph, between 4 to 6 seconds, the change in position of the object is constant, hence the velocity of the object will be zero, so we can conclude that the object is at rest between 4 to 6 seconds.

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The energy that is transferred as heat if the process is adiabatic is 0J and the work is done on or by the gas is 344J.

Given the internal energy of a gas decreases by (ΔU) = 344J

In an adiabatic process, an ideal gas' internal energy reduces by an amount equal to the work the system performs.

ΔU = work done + heat exchange

There is no heat exchange in an adiabatic process according to first law of thermodynamics.

The gas is doing work since the process is adiabatic and the amount of energy transferred as heat will be Q= 0J. If there is no heat exchange during the operation, a change in internal energy equals work done.

Then the work done by the gas is (W) = 344J

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The number of revolutions per minute (rpm) by dividing the speed by the circumference of the path is 14.89 rpm.

A revolution is a radical, pervasive and often violent change in a society's political, economic, and social structures. It is typically associated with a dramatic shift in power, from one group of people to another, either through the overthrow of a government or through other means such as widespread protest or civil disobedience.

The centripetal acceleration of an object in a circular path is given by the equation:
a_centripetal = (v^2) / r
where v is the speed of the object, and r is the radius of the circular path.
We know the radius of the path is 5.00 m and the centripetal acceleration should be 1.90 times that due to gravity. The acceleration due to gravity is 9.8 m/s^2. Therefore, the centripetal acceleration should be:
a_centripetal = 1.90 * 9.8 = 18.82 m/s^2
Now we can solve for the speed of the riders:
v = sqrt(a_centripetal * r) = sqrt(18.82 * 5.00) = 12.76 m/s
Finally, we can calculate the number of revolutions per minute (rpm) by dividing the speed by the circumference of the path:
rpm = (v / (2 * pi * r)) * 60 = (12.76 / (2 * pi * 5.00)) * 60 = 14.89 rpm.

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The correct statement would be that the wavelength is 2L and there is a displacement node at the pipe's mid point, if L is the length of the open pipe.

The fundamental frequency is the smallest resonant frequency of a vibrating object. Most of the vibrating objects possess more than one resonant frequency and which are used in musical instruments. On the other hand, a harmonic is defined as an integer multiple of the fundamental frequency.

Vibrating strings, open pipe, and conical air columns vibrate at all harmonics of the fundamental. Cylinders with only one end opened vibrate with only odd harmonics of the fundamental.

Hence the correct option is A.

--The given question is incomplete, the complete question is:

"The pipe of length L that is open at both ends is resonating at its fundamental frequency. which statement about sound is correct? A) The wavelength is 2L and there is a displacement node at the pipe's mid point. B) the wavelength is L and there is a displacement antinode at the pipe's mid point C) the wavelength is 2L and there is a displacement antinode at the pipe's mid point D) the wavelength is L and there is a displacement node at the pipe's mid point

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The intended receiver did not receive the ball since the ball travelled a shorter distance.

The time of motion of the ball is calculated by applying the following formula as shown below.

h = vt + ¹/₂gt²

where;

1.3 = ( 15.2 x sin40 )t  +   ¹/₂ ( 9.8 )(t²)

1.3 = 9.8t  +  4.9t²

4.9t² + 9.8t - 1.3 = 0

solve the quadratic equation suing formula method;

t = 0.13 second

The horizontal distance of the ball is calculated as;

d = Vₓt

d = ( 15.2 x cos 40) x 0.13

d = 1.51 m

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