Question

With what initial velocity must an object be thrown upward from a height of 2 meters to reach a maximum hieght of 200 meters

Answer 1

The equations of motion to use for a constant acceleration a = g = -9.81:

`v = gt + v_0`

`y = (1)/(2) g t^(2) + v_0t + y_0`

at the highest point the velocity must be zero:

`0 = gt + v_0 \\ v_0 = -gt`
combine both equations:

`y = (1)/(2) (v_0^(2) )/(g) - (v_0^(2) )/(g) + y_0= -(1)/(2) (v_0^(2) )/(g) + y_0`
Solve for v₀:

`v_0 = √(2g(y_0 - y))`