Two identical balls are projected, one vertically up and the other at an angle of `30^(@)` to the horizontal, with same initial speed. The potential energy at the highest point is in the ratio:

Options

A. `4:3`
B. `3:4`
C. `4:1`
D. `1:4`

Answer

C

Explanation

Using equation of motion,
height reached by first body, `h_(1)=(u^(2))/(2g)`
height reached by second body, `h_(2)=(u^(2)sin^(3) 30^(@))/(2g)`
`=1/4xx(u^(2))/(2g)`
`:. h_(1):h_(2)=4:1`
As `PE prop height`
`:. (PE)_(1):(PE)_(2)=4:1`