. A boy wishes to throw a ball through a house via two small openings, one in the front and the other in
the back window, the second window being directly behind the first. If the boy stands at a distance of 5m
in front of the house and the house is 6m deep and if the opening in the front window is 5m above him
and that in the back window 2m higher, calculate the velocity and the angle of projection of the ball that
will enable him to accomplish his desire.
Answer:
1) The angle of projection of the ball is approximately 52.496° above the horizontal
2) The velocity with which the boy throws the ball to enable him accomplish his desire is approximately 14.769 m/s
Explanation:
In the projectile motion of the ball, the parameters are;
The distance the boy stands from the front of the house = 5 m
The depth of the house, front to back = 6 m
The height of the opening of the front window above him = 5 m
The height of the back window = 2 m higher than the front window
Therefore, the height of the back window = 5 m + 2 m = 7 m
1) The general formula for the vertical height of a parabolic projectile motion is given as follows;
y = a·x² + b·x + c
At y = 0, x = 0, therefore, c = 0
At y = 5, x = 5, we have;
5 = a·5² + b·5
∴ 5 = 25·a + 5·b...(1)
At y = 7, x = 11, we have;
7 = a·11² + b·11
7 = 121·a + 11·b...(2)
Making 'a' the subject of equation (1) and (2) and equating both values of 'a' gives;
For equation (1);
a = (5 - 5·b)/25 = 1/5 - b/5
a = 1/5 - b/5
For equation (2);
a = (7 - 11·b)/121 = 7/121 - b/11
a = 7/121 - b/11
∴ 1/5 - b/5 = 7/121 - b/11
1/5 - 7/121 = b/5 - b/11
86/605 = 6·b/55
b = (86/605) × (55/6) = 43/33
b = 43/33
a = 1/5 - b/5 = 1/5 - (43/33)/5 = -2/33
∴ y = (-2/33)·x² + (43/33)·x
The slope of the curve = dy/dx = d((-2/33)·x² + (43/33)·x)/dx = -4/33·x + 43/33
The slope of the curve at any point on the projectile = -4/33·x + 43/33
The slope at the origin is given by plugging x = 0 as follows
The slope at the origin = -4/33 × 0 + 43/33 = 43/33
The slope at the origin = tan(θ) = 43/33
Where;
θ = The angle of projection of the ball
∴ θ = arctan(43/33) ≈ 52.496°
The angle of projection of the ball, θ ≈ 52.496° above the horizontal
2) At the back widow, the equation for the vertical height, 'h', is given as follows;
[tex]h = (tan \angle \theta) \cdot x - \left(\dfrac{g}{2 \cdot v_1^2 \cdot cos^2 \angle \theta } \right )\cdot x^2[/tex]
Where;
h = The vertical height of the back window = 7 m
tan∠θ = 43/33
x = The horizontal distance of the back window from the boy = 5 m + 6 m = 11 m
g = The acceleration due to gravity = 9.8 m/s²
v₁ = The velocity with which the boy throws the ball
cos²∠θ = cos²(arctan(43/33)) = 1089/2938
Plugging in the values gives;
[tex]7 = \left (\dfrac{43}{33} \right) \times 11 - \left(\dfrac{9.8}{2 \cdot v_1^2 \cdot \dfrac{1089}{2938} } \right )\cdot 11^2[/tex]
[tex]\therefore v_1^2 = \dfrac{71981}{330}[/tex]
[tex]\therefore v_1 = \sqrt{\dfrac{71981}{330}} \approx \pm14.769[/tex]
The velocity with which the boy throws the ball to enable him accomplish his desire, v₁ ≈ 14.769 m/s.
4. Premature wrinkling due to overexposure to the Sun, what am I?
Premature Aging
Mark as brainlist
in a nuclear plant, 1 * 10 ^27 J of energy is available from mass conversion How much mass was lost ?
Answer:
[tex]1.2\times 10^{10}\ kg[/tex]
Explanation:
Given that,
The energy of the nuclear plant, [tex]E=10^{27}\ J[/tex]
We need to find how much mass wast lost.
The relation between energy and mass is given by :
[tex]E=mc^2[/tex]
Where
c is speed of light
[tex]m=\dfrac{E}{c^2}\\\\m=\dfrac{10^{27}}{(3\times 10^8)^2}\\\\m=1.2\times 10^{10}\ kg[/tex]
So, [tex]1.2\times 10^{10}\ kg[/tex] of mass was lost.
4. A substance is cut into several piece and compared to the density of the
original sample. The density of each piece will be:-
areater
bl the same
Answer:
The density pf each piece will be the same, since density is defined as a mass per unit volume, so even when you cut an object it will not change
Which of the following determines the identity of an atom?
A. atomic mass
B. mass number
C. atomic number
D. charge
A scientist performed an investigation involving a reaction that produced AI, (SO )3. How many sulfur atoms are
represented in this formula?
Answer:
D
Explanation:
Because you add them all up it equals 9
1/2 means that the voltage (or charge) of the system will increase to half more of what is left in a time equal to t1/2 seconds. Therefore if a system is already at half charge (t1/2 seconds after starting) then after t1/2 more seconds the system will be charged to 50% plus half of 50%. That is 25% more, or 75% of the entire charge. Let's say that four t1/2's have gone by. That means that the charge (or voltage) is at (50% + 1/2*50% + 1/2*1/2*50% + 1/2*1/2*1/2*50%) = 93.75% of maximum charge. Yikes! Now look in your manual for a more simple mathematical derivation of this concept. Given t1/2 to be 0.4406 seconds, how long should it take to reach 75% of maximum charge? answer in seconds.
Answer:
The answer is "0.047".
Explanation:
Given value:
[tex]\to t_{\frac{1}{2}}= 0.4406\\\\\to V=0.9375 V_{max}[/tex]
Calculating the capacitance:
[tex]\to V=V_{max} (1-e^{\frac{-t}{Rc}})[/tex]
In this, the t = time, which is taken to calculates its maximum voltage.
[tex]\to 0.9375 V_{max} = V_{max}(1-e^{- \frac{t}{103\times(165.279\times10^{-6})}})\\\\\to e^{- \frac{t}{103\times(165.279\times10^{-6})}}= 0.0625\\\\\to - \frac{t}{103\times(165.279\times10^{-6})} = \ln(0.0625)\\\\\to -t= 0.01702\times(-2.77258) \\\\ \to -t = -0.04719 \\\\ \to t= 0.04719 \approx 0.047 \ s[/tex]
On which factor does the inertia of a body depend?
Answer:
The moment of inertia depends on the following factors, The density of the material. Shape and size of the body. Axis of rotation (distribution of mass relative to the axis)
1. Electrons spinning around the nucleus of an atom cause the atom to
a. be a tiny magnet.
b. have north and south poles.
c. have a magnetic field.
d. all of the above
Answer:
Answer:answer is C
is the magnetic field
1. A plane mirror has a
surface
Answer:
A plane mirror is a mirror with a flat (planar) reflective surface. For light rays striking a plane mirror, the angle of reflection equals the angle of incidence. The angle of the incidence is the angle between the incident ray and the surface normal (an imaginary line perpendicular to the surface).
which of these is NOT a metamorphic rock?
Basalt
Slate
Marble
Explanation:
Basalt is not a metamorphic rocks
Which of the following will best transport electrons around an electrical circuit
Answer:
b is correct!!!!!!!!!!!
The best transport electrons around an electrical circuit are connected in series. Thus, the correct answer would be option (B) are connected in series.
What is alternating current (AC)?An alternating current (AC) circuits continuously switches the direction of electron flow back and forth, which can result in fluctuations in voltage and current.
On the other hand, in a direct current (DC) electrical circuit, the electrons flow in one direction, from the negative terminal of the power source to the positive terminal. This unidirectional flow of electrons provides a consistent and stable flow of electricity throughout the circuit.
Connecting components in series mean that they are connected end-to-end, and the current flowing through them is the same.
Overall, the best option to transport electrons around an electrical circuit are to connect in series.
Therefore, the correct answer would be option (B) are connected in series.
Learn more about alternating current (AC) here:
https://brainly.com/question/28305485
#SPJ6
The final velocity of a car is 30m/s. The car is accelerating at a rate of 2.5m/s2
over an 2.8m/s2
8 second period of time. What is the initial velocity of the car?
Answer:
10m/s
Explanation:
Vf=v0+at
30m/s=v0+2.5m/s^2*8s
Solve for v0=10m/s
Sorry for the vague explanation I'm on my phone right now. Hope this still helps!
Initial velocity of the car where final velocity of a car is 30m/s and it is accelerating at a rate of 2.5 [tex]m/s^{2}[/tex] over an 2.8 [tex]m/s^{2}[/tex] 8 second period of time is 10 m/s.
To find the initial velocity of the car, we can use the kinematic equation:
Final velocity (v) = Initial velocity (u) + (Acceleration (a) * Time (t)).
Given the final velocity (v) as 30 m/s, acceleration (a) as 2.5 [tex]m/s^{2}[/tex], and time (t) as 8 seconds, we can plug these values into the equation:
30 m/s = u + (2.5 [tex]m/s^{2}[/tex] * 8 s).
Now, solve for the initial velocity (u):
30 m/s = u + 20 m/s.
Subtract 20 m/s from both sides:
u = 30 m/s - 20 m/s = 10 m/s.
Therefore, the initial velocity of the car is 10 m/s.
To know more about Initial velocity, here
brainly.com/question/28395671
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What is the direction of the force of an object moving in a circle?
1.toward the center of the circle
2.toward the outside of the circle
3.straight up
4.45 degree angle
Answer:
The answer is 45 degree angle
HELP please!!!!!!!!!!!!!!!
An object has a mass of 3 kg and an acceleration 7 m/s2to the left. What is the force?
Answer:
your answer is 21 n
Explanation:
HELP ASAP!!! The gravitational pull of the Moon is much less than the
gravitational pull of Earth.
Which two statements are true for an object with a mass of 20 kilograms that
weighs 44 pounds on Earth?
O A The object's weight would be the same on the Moon
B. The object's weight would be less on the Moon
C. The object's mass would be the same on the Moon
DD. The object's mass would be less on the Moon
Answer:
I'm pretty sure its B and C
Explanation:
B bc the weight is gravitational pull x mass so when the object has same mass the weight is smaller on moon
C bc mass is the same - you can't change it
The correct answers are B and C
Which has more potential energy: a baseball held 1 m above the ground or a baseball held 2 m above the ground?
The baseball held 2 meters above the ground has more potential energy than the baseball held 1 meter above the ground.
The potential energy can be calculated with the following equation:
[tex] E_{p} = mgh [/tex]
Where:
m: is the mass of the baseball
g: is the acceleration due to gravity
h: is the height
We can see from equation (1) that the potential energy depends on height, mass, and gravity. Since the question refers to the same baseball, the mass is constant besides the acceleration due to gravity, so:
Potential energy above 1 m[tex] E_{p_{1}} = mg*1 = mg [/tex] (1)
Potential energy above 2 m[tex] E_{p_{2}} = mg*2 = 2mg [/tex] (2)
By entering equation (1) into 2 we have:
[tex] E_{p_{2}} = 2mg = 2E_{p_{1}} [/tex]
Hence, the potential energy of the baseball held 2 m above the ground is twice that of the baseball held 1 m above the ground.
Therefore, the baseball held 2 m above the ground has more potential energy.
You can learn more about potential energy here: https://brainly.com/question/15813853?referrer=searchResults
I hope it helps you!
A human cannonball act uses springy bungee cords instead of gunpowder to launch a person through a long cylindrical tube into the air. If a cannon is capable of launching a 55 kg test dummy 11 m into the air when launched straight up, how much energy is stored in the bungee cords? *
A. 539J
B. 605 J
C. 2965J
D. 5929 J
Answer:
Energy stored, E = 5929 J
Explanation:
Given that,
The mass of a test dummy, m = 55 kg
It is launched 11 m into the air.
We need to find the energy stored in the bungee cords. It can be calculated as follows :
[tex]E=mgh\\\\E=55\times 9.8\times 11\\\\E=5929\ J[/tex]
So, 5929 J of energy is stored in the bungee cords.
guys pls thi is my last pointa just answer this!!!!(WILL GIVE BRAINLY) A student takes apart a wooden box. What can they build with the materials from the box?
A) They cannot make anything with the materials.
B) They can make something new with the materials.
C) They can only make a wooden box from the materials.
Answer:
i guess u could pick "B" :)
Explanation:
Anyone able to help with these questions, will give brainliest to first correct anwser
Answer:
b
Explanation:
I did this question earlier
An electric iron is connected to the mains power supply of 220 V. When the electric iron is
adjusted at 'minimum heating' it consumes a power of 360 W but at 'maximum heating' it takes a
power of 840 W. Calculate the current and resistance in each case.
Answer:
Given: V = 220V, Pmin = 360W, Pmax = 840W
For minimum heating case:
We know that
Pmin = VI
360 = 220 X I
I = 1.63 amp
R = V/I
R = 220/1.63
R = 134.96ohms
For maximum heating case:
We know that
Pmax = VI
840 = 220 X I
I = 3.81 amp
R = V/I
R = 220/3.81
R = 57.74 ohms
What term is defined as speed with a specific direction?
velocity
position
distance
displacement
Answer:
Velocity
Explanation:
I took the test.
A student wants to make an analogy to help her remember the characteristics of the planets. Which analogy makes the most sense?
The inner planets are like cotton candy and the outer planets are like hard butterscotch candy.
The outer planets are like bowling balls and the inner planets are like basketballs.
The inner planets are like hard butterscotch candy and the outer planets are like cotton candy.
The outer planets are like roses and the inner planets are like daisies.
Answer:
The last one makes the most sense as they combine two like things that are easy to visualize
Explanation:
Answer:
C. The inner planets are like hard butterscotch candy and the outer planets are like cotton candy.
Explanation:
Right on ED2021, goodluck!
PLEASE HELP PLEASEEEE
Answer:
Concave mirror
Explanation:
Because as we move the object far away from the mirror the image gets inverted
34 Which of these human characteristics shows discontinuous variation?
A blood group
B hair color
C height
D weight
Answer:
Blood group
Explanation:
Answer:
A. Blood group.
Explanation:
They could purely random genetic changes.
how important is it to have an emergency plan
Answer:
The actions taken in the initial moments after a crisis matter. These steps can determine how disruptive the aftermath will be. With this in mind, companies need to plan for any potential incidents that could occur. In this blog post, we discuss the importance of emergency planning, the impact it has on a crisis and how to prepare for the worst.
Explanation:
hope you like it
Which graph shows a vehicle traveling at a constant speed?
(look at the attached photo)
1.) A projectile is launched at 32.1 m/s and 52.6 º above the horizontal. Determine the:
a.) Maximum height of the projectile.
b.) The time it takes to reach the maximum height
c.) Time of flight
d.) Range
Answer:
a.) Maximum height of the projectile. =32.5m
b.) The time it takes to reach the maximum height=2.6s
c.) Time of flight=2.6s
d.) Range=99.5m
Explanation:
Please help me, I'm not good in physics.
You press your physics textbook flat against a vertical wall with your hand. What is the direction of the friction force exerted by the wall on the book? (a) downward (b) upward (c) out from the wall (d) into the wall. (Serway and Jewett, 2009) What type of friction is present?
Answer:
Upward direction.
The friction is kinetic friction