1. You are walking around your neighborhood and you see a child on top of a roof
ID: 1280478 • Letter: 1
Question
1. You are walking around your neighborhood and you see a child on top of a roof of a building kick a soccer ball. The soccer ball is kicked at 31 from the edge of the building with an initial velocity of 21 m/s and lands 61 meters away from the wall. How tall is the building that the child is standing on?
_____ m
2. You are sitting in the back of a produce truck that has stopped at a red light. You want to measure its acceleration when the light turns green. You could actually measure the acceleration of the truck by measuring the increase in weight of a mass with a spring scale. You decide to hang a large potato on a spring scale. It weighs 4.6N. The light turns green. The truck begins to accelerate. As the truck accelerates apparent weight of the large potato increases to 5.03N as it swings from the vertical.
(a) To what angle does the potato swing from the vertical?
________ o
(b) What is the acceleration of the truck?
________ m/s/s
3. Consider the 49.0 kg mountain climber in the figure below.
(a) Find the tension in the rope and the force that the mountain climber must exert with her feet on the vertical rock face to remain stationary. Assume that the force is exerted parallel to her legs. Also, assume negligible force exerted by her arms.
(b) What is the minimum coefficient of friction between her shoes and the cliff?
66.59 DID NOT WORK AS THE ANSWER
Explanation / Answer
LOL. Only a physicist would see a child kick a ball from a roof and wonder about the initial velocity of the ball and the height of the roof. Anyone else would tell the child to get down before he hurt himself!
However a physicist would be thinking:
Ignoring air resistance:
Vx0 = V0 cos theta = 21m/s cos 31 degrees = 18 m/s
Vy0 = V0 sin theta = 21 m/s sin 31 degrees = 11 m/s
So how long does it take the ball to travel 61 meters along the x axis?
s = ut
61m = 18m/s t
t = 61m/18m/s = 3.4 seconds.
We now know the total flight time of the ball was 3.4 seconds.
What about it's height?
Sy - Sy0 = ut + (1/2)at^2
where Sy0 is the initial distance up the y axis (ie the height of the roof that we want to find).
Sy is the final height of the ball (i.e. ground level)
u is the initial velocity along the y axis
a is the acceleration (in this case gravity g = -9.8 m/s^2)
t is the total flight time.
slightly rearranging
-Sy0 = -sy + ut + (1/2)at^2 but sy = 0 anyway and a = -g
but sy = 0
-Sy0 = ut - (1/2) gt^2
-Sy0 = (11 m/s) (3.4 s)- (1/2)(9.8 m/s^2) (3.4s)^2
by calculator
-Sy0 = -19 meters.
Sy0 = 19 meters.
So the naughty child is on a roof that is 19 meters tall.
So as a physicist your response should be to explain to the boy exactly how much force will be exerted on his bones if he falls off the roof using F = ma.
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