Question

A body is projected at an angle of $60^\circ $ with the horizontal. If its kinetic energy at its maximum height is $10 \, J$ , then the height at which its potential energy and kinetic energy have equal values is (consider potential energy at the point of projection to be zero)

• A. half of the maximum height
• B. two third of the maximum height
• C. one sixth of the maximum height
• D. insufficient data to solve the problem

Answer 1

Answer: (B)

KE at maximum height
$\frac{1}{2} \text{mu}^{2} \text{cos}^{2} 6 0^{^\circ } = 1 0 J$
$\frac{1}{2} \text{mu}^{2} = 4 0 J$
$Mg \text{H}_{\text{max}} = 3 0 J$ ...(i)
When $\text{PE} = \text{KE}$
$⇒ \, \, \, \text{mgh} = 2 0 =$ ...(ii)
from (i) and (ii)
$\frac{\text{h}}{\text{H}_{\text{max}}} = \frac{2}{3}$