Question

A body is projected at an angle of ${60}^0$ with the horizontal. If its kinetic energy at maximum height is 10 J, then the height at which potential energy and kinetic energy have equal values (consider P.E. at the point of projection to be zero) is :

• 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

The correct option is B two third of the maximum height

KE at maximum height
$\frac{1}{2}{mu}^2{\cos }^2{60}^0=10J$
$\frac{1}{2}{mu}^2=40J$

The above equation is the kinetic energy at the lowest point and hence the total energy of the particle.

At the highest point, total energy is:

$mg{h}_{max}+KE=40$

$mg{h}_{max}+10=40$
$mg{h}_{max}=\mathrm{30..............}\left(1\right)$

When $PE=KE$
$PE=20=KE$
$\Rightarrow mgh=20............\left(2\right)$
From (1) and (2),
$\frac{h}{h_{max}}=\frac{2}{3}$