Physics 198
Homework 3
Due September 3
1. A stone is dropped from the top of a cliff. It hits the ground below after 3.25 s. How high is
the cliff?
Solution:
Choose upward to be the positive direction, and take y = 0 at the bottom of the cliff. The initial
velocity is v0  0 . The height of the cliff y 0 is found from equation
gt 2

2
y  y 0  v0 t 
y0 
9.8m / s 3.25s 
2
2
0  y0 
gt 2

2
y0 
gt 2
2
2
y0  51.8m

2. From the same height (and at the same time), one ball is dropped and another ball is fired
horizontally. a) Which one will hit the ground first? b) Which ball has the greater velocity at
ground level? (Explain)
Solution:
a) Both of the balls are falling vertically under the influence of gravity. They both fall from the
same height. Therefore, they will hit the ground at the same time. The fact that one is
moving horizontally is irrelevant – remember that the x and y motions are completely
independent!!
b) Both balls have the same vertical velocity when they hit the ground (since they are both acted
on by gravity for the same time). However, the “fired” ball also has a horizontal velocity.
So, the “fired” ball has a larger net velocity when it hits the ground.
3. The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t
the heavier rock fall faster?
Solution: The acceleration of both rocks is found by dividing their weight (the force of gravity on
them) by their mass. The 2-kg rock has a force of gravity on it that is twice as great as the force
of gravity on the 1-kg rock, but also twice as great a mass as the 1-kg rock, so the acceleration is
the same for both.
4. Find weight of a 2-kg rock. The rock is located in Ames.


Solution: Weight: Fg  mg  2kg 9.8m / s 2  19.6 N
5. What force should be applied to move a 2-kg rock with acceleration equal one half of
acceleration due to the gravity (g/2).


Solution: F  ma  mg / 2  2kg 9.8m / s 2 / 2  9.8N
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