Question

Two students are on a balcony a distance h above the street. One student throws a ball vertically downward at a speed vi; at the same time, the other student throws a ball vertically upward at the same speed. Answer the following symbolically in terms of vi, g, h, and t. (Take upward to be the positive direction.)
(a) What is the time interval between when the first ball strikes the ground and the second ball strikes the ground?
Δt =

(b) Find the velocity of each ball as it strikes the ground.
For the ball thrown upward vf =
For the ball thrown downward vf =

(c) How far apart are the bal

Answer 1

Part (a):
\[{h} = v _{i} t + \frac{ 1 }{ 2 } gt ^{2}\] This equation will help solve the first part. You know initial vertical displacement h, initial vertical velocity vi, and acceleration due to gravity g. So you would simply time t for each ball. Remember to change signs for directions! Subtract one from the other for the difference.

Part (b):
\[v ^{2}_{f} = v ^{2}_{i} + 2gh\] This equation will help solve for the second part. You know initial vertical displacement h, initial vertical velocity vi, and acceleration due to gravity g. Simply solve for vf.

Part (c):
I won't even dive into this part. If you solved for the time differential, then this should follow from that!

Good Luck!