A ball is projected vertically upwards with a certain initial speed. Another ball of the same mass is projected at an angle of `60^(@)` with the vertical with the same initial speed. At highest points of their journey, the ratio of their potential energies will be

Options

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

Answer

D

Explanation

In verticle upwards. PE=mgh
`=mg((V_(2))/(2g))=(mv^(2))/(2)`...(i)
at an angle of `60^(@)` with vertical PE=mgh
`=mg((V^(2)sin^(2)30^(@))/(2g))=(mv^(2))/(8)`....(ii)
From (i)/(ii). `((PE)_(up))/((PE)_("at" theta=60^(@)"fromvt.))=((mv^(2))/(2))/((mv^(2))/(8))=(4)/(1)`