Question

A ball is projected at an angle of \( 45^\circ \) with the horizontal. It passes through a wall of height \( h \) at a horizontal distance \( d_1 \) from the point of projection and strikes the ground at a distance \( d_1 + d_2 \) from the point of projection, then \( h \) is:

• A. \( \frac{2d_1 d_2}{d_1 + d_2} \)
• B. \( \frac{d_1 d_2}{d_1 + d_2} \)
• C. \( \frac{\sqrt{2} d_1 d_2}{d_1 + d_2} \)
• D. \( \frac{d_1 d_2}{2(d_1 + d_2)} \)

Hint:

For projectile motion, the height at any point can be found using the trajectory equation. The choice of reference points simplifies calculations.

Answer 1

The Correct Option is B

Step 1: Use projectile motion equation. The equation of the projectile is given by: \[ y = x \tan \theta - \frac{gx^2}{2u^2 \cos^2\theta} \] Since \( \theta = 45^\circ \), we substitute and rearrange for \( h \): \[ h = \frac{d_1 d_2}{d_1 + d_2} \]