A bullet fired at an angle of `30^@` with the horizontal hits the ground 3.0 km away. By adjusting its angle of projection, can one hope to hit a target 5.0 km away? Assume the muzzle speed to be fixed and neglect air resistance.

Explanation

We are given that angle of projection with the horizontal, `theta=30^(@)`, horizontal range `R=3km`.
`R=(u_(0)^(2)sin 2 theta)/g`
`3=(u_(0)^(2)sin 60^(@))/g=u_(0)^(2)/gxxsqrt3/2`
`or u_(0)^(2)/g=2sqrt3km`
Since the muzzle speed `(u_(0))` is fixed
`R_(max)=(u_(0)^(2))/g=2sqrt3=2xx1.732=3.464km`
so,it is not possible to hit the target `5km` away.