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
$\therefore mg{h}_1=\frac{1}{2}m{u}^2$
or $h_1=\frac{u^2}{2g}$
For second ball
$mg{h}_2=\frac{mg{u}^2{\sin }^2\theta }{2g}$
$=\frac{1}{2}m{u}^2{\sin }^{2}30^{\circ }$
$=\frac{1}{2}m{u}^2{\left(\frac{1}{2}\right)}^2$
or $h_2=\frac{u^2}{8g}$
$\therefore \frac{h_1}{h_2}=\frac{u^2}{2g}\times \frac{8g}{u^2}$
$\Rightarrow \frac{h_1}{h_2}=\frac{4}{1}$