Question
A ball is projected from the ground at 45°. It strikes
a vertical wall and rebounds with the same speed making the same angle on the other side. If the wall is at a distance R/2, where R is the total range, what is the total time of flight?Solution
We are given:
- A ball is projected at 45° and rebounds with same speed and same angle after hitting a vertical wall.
- The wall is located at R/2, where R is the total horizontal range of the projectile if no wall were present.
- We are to find the total time of flight after hitting and rebounding.
- At R/2, the ball is at half the horizontal range, so the time to reach wall is T/2, where T is the total time of flight without the wall.
- Total time of flight without wall:
T = 2u·sinθ / g = 2u·(1/√2) / g = (2u)/(√2·g) = √2·u/g
- The ball reverses horizontal direction, but keeps same speed and same 45° angle (as per question).
- So its remaining path is a mirror image of the first half.
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