Question

If a ball released from a height \(H\) takes a time \(T\) to reach the ground, then the position of the ball from the ground at a time \(\frac{T}{2}\) is:

• A. \(\frac{H}{4}\)
• B. \(\frac{H}{2}\)
• C. \(\frac{3H}{4}\)
• D. \(\frac{2H}{3}\)

Hint:

At half the time of fall, object covers one-fourth distance; remaining height is three-fourths.

Answer 1

The Correct Option is C

Using equation for free fall: \[ H = \frac{1}{2}gT^2 \Rightarrow T = \sqrt{\frac{2H}{g}} \] Displacement after \(\frac{T}{2}\): \[ s = \frac{1}{2}g \left(\frac{T}{2}\right)^2 = \frac{1}{2}g \times \frac{T^2}{4} = \frac{1}{4} \times \frac{1}{2} g T^2 = \frac{H}{4} \] Height from ground at \(\frac{T}{2}\): \[ H - s = H - \frac{H}{4} = \frac{3H}{4} \]