I drop a ball (from rest) from the fourth floor of a building (at height 4h above the ground). After the ball has fallen a distance d, my friend drops a second ball (again from rest) from the first floor (at height h). Assume that there is enough horizontal separation between the two balls that they do not collide. a) What should d be, in terms of h, so that both balls hit the ground at the same time? b) Assuming that the ground simply reverses the direction of the velocity vector of a ball hitting the ground, plot the vertical distance between the two balls as a function of time (after they have hit the ground at the same time). In particular, at what time are the two balls at the same height? What is the maximum distance between the two balls?

Question

I drop a ball (from rest) from the fourth floor of a building (at height 4h above the ground). After the ball has fallen a distance d, my friend drops a second ball (again from rest) from the first floor (at height h). Assume that there is enough horizontal separation between the two balls that they do not collide.

a) What should d be, in terms of h, so that both balls hit the ground at the same time?
b) Assuming that the ground simply reverses the direction of the velocity vector of a ball hitting the ground, plot the vertical distance between the two balls as a function of time (after they have hit the ground at the same time). In particular, at what time are the two balls at the same height? What is the maximum distance between the two balls?

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