A car 2m long and 3m wide is moving at `10m//s` when a bullet hits it in a direction making an angle of `tan^(-1)(3//4)` with the car as seen from the ground. The bullet enters one edge of the car at the corner and passes out at diagonally opposite corner. Neglecting gravity, the time for the bullet to cross the car is

Explanation

Bullet enters at `O` and emerges at `A`.
`v_("bullet"//"ground")=v`
`v_(car//g)=10 m//s`

`(v_(b//c))_(x)=v cos theta-10, (v_(b//c))_(y)=v sin theta` (now car is at rest)
`x:` (uniform motion): `(v cos theta-10)t=2.......(i)`
`y:` (uniform motion): `v sin theta t=3.......(ii)`
Dividing (i) and (ii), we get
`(v cos theta-10)/(v sin theta)=2/3 implies (vxx4/5-10)/(vxx3/5)=2/3`
`v=25m//s`
`v sin theta t=3`
`25xx3/5 t=3 implies t=1/5 =0.2 s`