A trolley having a cannon fixed to it which can shoot only vertically, is moving with a velocity `v_(0) = 12 m//sec` in horizontal direction. At a certain instant, it is at a distance of `120 m` front a balloon which is held on ground and now it is released. The balloon starts rising with constant velocity `2v_(0)`. Calculate the minimum veloctiy of cannon ball so that it can hit the balloon.

Options

A. `74 m//s`
B. `37 m//s`
C. `148 m//s`
D. `222 m//s`

Answer

A

Explanation

Time taken by ball A is covering distace x.
`t_(0) = x//v_(0) = 120//12 = 10 sec`
Height moved by balloon, `h = 2v_(0)t_(0) = 240` in time `t_(0)` ball A also moves a heght h.

`h = v_(y) t_(0) - 1//2t_(0)^(2)`
`240 = v_(y) xx 10 - 1//2 xx 10 xx 100`
`v_(y) = 74 m//s`