Three small heavy balls are dropped from rest at the same time, but from differe

Question

Three small heavy balls are dropped from rest at the same time, but from different heights. The lowest ball is dropped from height h; the middle ball is dropped from a distance a above the lowest ball (so h + a above the ground level). The top ball is dropped from a distance b above the middle ball (so h + a + b above ground level.) Your task is to determine the relationship between a and b such that the time difference between when the lowest and middle ball hit the ground and the time difference between when the middle and top ball hit the ground are the same.

a) Draw some physical representation (motion diagram or graph) that allows you to determine qualitatively whether a = b, a < b or a > b. Clearly show/explain which one of these you believe.
b) How long will it take the lowest ball to hit the ground if it starts from a height of 1.0 m. (You must solve this in variables first (i.e., an equation without numbers) for full credit.)
c) If a = 30.0 cm, find b such that the time difference is the same between when the lowest and middle ball hit and between when the middle and top ball hit. (You must solve this in variables first (i.e., equation(s) without numbers) for full credit.)
d) Is your numerical answer in agreement with your earlier physical representation answer?

Explanation / Answer

a. h= 1/2 g t1^2
1 = 5 *t1^2
t1^2 = 0.2
t1 = 0.45s

b. h+a = 1/2 g t2^2
1.3 = 1/2*10*t2^2
1.3 = 5*t2^2
t2= 0.51s

the time difference between when the lowest and middle ball hit the ground and the middle and top ball hit the ground are the same, so
t2- t1 = t3 - t2
0.51 - 0.45 = t3 -0.51
t3 = 0.57s
subsitute t3 = 0.57 to h+a+b = 1/2 g t3^2
1.3 +b = 5* 0.57^2
1.3 +b = 1.62

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