A bullet fired at an angle of 30^(@) with the horizontal hits the ground 3.0km 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.

A bullet fired at an angle of 30^(@) with the horizontal hits the grou

1.	A bullet fired at an angle of 30^(@) with the horizontal hits the ground 3.0km 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.
Answer» Solution :We are GIVEN that angle of projection with the horizontal, `theta=30^(@)`, horizontal range `R = 3km`. As `R=(v_(0)^(2)SIN2THETA)/(g),3=(v_(0)^(2)sin60^(0))/(g)=(v_(0)^(2))/(g)xx(sqrt(3))/(2)` or `(v_(0)^(2))/(g)=2sqrt(3)km` SINCE the muzzle speed `(v_(0))` is fixed, `R_(max)=(v_(0)^(2))/(g)=2sqrt(3)=2xx(1.732=3.464km` Obviously, it is not possible to hit the target 5km away.