A body is projected at an angle of 60° 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)

Question

A body is projected at an angle of 60° 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

Tardigrade Admin · Accepted Answer

KE at maximum height (1/2) textmu2 textcos2 6 0° = 1 0 J (1/2) textmu2 = 4 0 J Mg textH textmax = 3 0 J ...(i) When textPE = textKE â textmgh = 2 0 = ...(ii) from (i) and (ii) ( texth/ textH textmax) = (2/3)

Q. A body is projected at an angle of $6 0^{\circ}$ 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)

half of the maximum height

two third of the maximum height

one sixth of the maximum height

insufficient data to solve the problem

KE at maximum height
$\frac{1}{2} mu^{2} cos^{2} 6 0^{^{\circ}} = 10 J$
$\frac{1}{2} mu^{2} = 40 J$
$M g H_{max} = 30 J$ ...(i)
When $PE = KE$
$\Rightarrow mgh = 20 =$ ...(ii)
from (i) and (ii)
$\frac{h}{H _{max}} = \frac{2}{3}$

Q. A body is projected at an angle of 60∘ with the horizontal. If its kinetic energy at its maximum height is 10J , 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)