Question

A stone is dropped from a bridge into the water below with a speed of 20m/s. a second stone is thrown vertically downward when the first stone is halfway to the water. If both stones strike the water at the same time, what was the initial velocity of the second stone?

Answer 1

$$h=vt+0.5gt^2\to h=vt+5t^2$$

$$h=20(t+t_1)+0.5g(t+t_1)^2\to h=20(t+t_1)+5(t+t_1)^2$$

$$0.5h=20t_1+5t_1^2$$

$$0.5h=(20+10t_1)t+5t^2$$

So, we need the height of the bridge for final calculations.