Question

A particle is fired from `A` in the diagonal plane of a building of dimension `20m`(length) `xx` `15m` (breadth) `xx` `12.5 m`(height), just clears the roof diagonally & falls on the other side of the building at `B`.It is observed that the particle is travelling at an angle `45^(@)` with the horizontal when it clears the edges `P` and `Q` of the diagonal. Take `g=10m//s^(2)`.
The speed of projection of the particle at `A` will be:

A. `5sqrt10m//s`
B. `10sqrt5m//s`
C. `5sqrt15m//s`
D. `5sqrt5m//s`

Answer 1

Correct Answer - B
`V_(y)^(2)-U_(y)^(2)=2a_(y)S_(y)`
`125-(U sin theta)^(2)=-2(10)125 rarr (1)`
`5sqrt10 cos 45=V cos theta rarr(2)`
On solving `U=sqrt500m//s,theta=Tan^(-1)sqrt3=60^(@)`