Question

A ball is projected vertically upwards with a certain initial speed. Another ball of the same mass is projected at an angle of $60^{\circ}$ with the vertical with the same initial speed. At highest points of their journey, the ratio of their potential energies will be

• A. 1 : 1
• B. 2 : 1
• C. 3 : 2
• D. 4 : 1

Answer 1

Answer: (D)

For first ball At highest point, the kinetic energy is completely converted into its potential energy
$\therefore m g h_{1}=\frac{1}{2} m u^{2}$
or $h_{1}=\frac{u^{2}}{2 g}$
For second ball
$m g h_{2}=\frac{m g u^{2} \sin ^{2} \theta}{2 g}$
$=\frac{1}{2} m u^{2} \sin ^{2} 30^{\circ}$
$=\frac{1}{2} m u^{2}\left(\frac{1}{2}\right)^{2}$
or $h_{2}=\frac{u^{2}}{8 g}$
$\therefore \frac{h_{1}}{h_{2}}=\frac{u^{2}}{2 g} \times \frac{8 g}{u^{2}}$
$\Rightarrow \frac{h_{1}}{h_{2}}=\frac{4}{1}$