Answer
The ball should be thrown upwards with the speed of $31 ms^{-1}$.
Work Step by Step
Step-1: We need to throw a ball with velocity $v_0 ms^{-1}$ to cover a distance of $50m$ against acceleration due to gravity, which equals $-9.8ms^{-2}$. We know that when a ball is at its maximum height, its velocity at that instant is $0ms^{-1}$, that is, $v=0ms^{-1}$.
Step-2: For an ascending ball, $$v^2=v_0^2-2ax$$ $$(0)^2=v_0^2-2\times (9.8) \times 50$$ $$\implies v_0=\sqrt{980}=31.30ms^{-1} \approx 31 ms^{-1}$$
