A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?

Solution

Physics sir · 3 steps

Same arm, same throwing speed: get u²/g from the range, then throw straight up for maximum height.

1. Speed from range. The range R = (u² sin 2θ)/g is largest at θ = 45°, where sin 2θ = 1. So Rₘₐₓ = u²/g = 100 m.
2. Highest throw. The person throws with the same speed u. To go as high as possible, all of u must point upward, so the ball is thrown vertically.

   Hₘₐₓ = u²/2g = 1/2×u²/g = 1/2× 100 m = 50 m

3. So. The greatest height he can reach is Rₘₐₓ/2 = 50 m, which is option (b).

The idea to keep. For one fixed throwing speed, the greatest height you can reach is half the greatest range: Hₘₐₓ = u²/2g and Rₘₐₓ = u²/g.

Answer from the NTA final answer key. Solution by PrepWiser.