The angle of projection for a projectile to have same horizontal range and maximum height is :

Solution

Physics sir · 3 steps

Write R and H in terms of the angle, set them equal, and tan θ pops straight out.

1. Write both formulas. For speed u at angle θ, the range is R = (u² sin 2θ)/g = (2u² sin θ cos θ)/g. The maximum height is H = (u² sin² θ)/2g.
2. Set them equal. Put R = H. Then u² and g cancel from both sides, and one factor of sin θ cancels too, since sin θ ≠ 0.

   2 sin θ cos θ = (sin² θ)/2 ⇒ 4 cos θ = sin θ ⇒ tan θ = 4

3. So. The angle of projection is θ = tan⁻¹(4), which is option (d).

The idea to keep. Remember R = 4H/(tan θ) for any projectile on level ground. Any question comparing range and height becomes one line with this.

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