Question

A body of mass 50 g is projected vertically upwards from the ground. If the kinetic energy of the body at a height of 32 m is 100% more than its potential energy, then the height at which the potential energy of the body becomes 60% of its kinetic energy is

• A. 24 m
• B. 72 m
• C. 18 m
• D. 36 m

Hint:

For problems with vertical motion and energy ratios, always express KE and PE as fractions of total energy and solve algebraically for the height.

Answer 1

The Correct Option is D

1. Let total mechanical energy $E = KE + PE$. At h = 32 m, $KE = 2 \cdot PE \implies KE = \frac{2}{3}E$, $PE = \frac{1}{3}E$.
2. We need height $h$ where $PE = 0.6 KE \implies PE = 0.6 (E - PE) \implies PE = 0.375 E$.
3. $PE = m g h \implies h = 0.375 E / (m g)$. Using proportionality, $h = 36~\text{m}$.