Question

2) A diving platform or diving tower has three platforms at 10 m, 7.5 m, and 5.0 m. Some students are going to drop or throw straight down identical balls from each platform and they want the balls to reach the water with the same velocity. The ball from the highest platform will just be dropped with zero inital velocity. (a) What velocity do you need to throw the ball from the middle platform? (b) What velocity do you need to throw the ball from the bottom platform?

Answer 1

since the height h = Ho+Vo*t-4.9t^2,

the top ball will hit after t seconds, where

10+0t-4.9t^2 = 0
t = 1.429 seconds
its final speed is v = 0-1.429*9.8 = -14.00 m/s

The middle ball must then be thrown downward with velocity v such that

v-9.8t = -14.00
7.5+v*t-4.9t^2 = 0
v = -7 m/s

The low ball must satisfy

v-9.8t = -14.00
5.0+v*t-4.9t^2 = 0
v = -9.9 m/s