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

Here R = 3km = 3000m, `theta=30^(@)`, g`=9.8ms^(-2)`
As `R=(u^(2)sin2theta)/(g)`
`rArr 300= (u^(2)sin2 xx 30^(@))/(9.8) = (u^(2)sin60)/(9.8)`
Also, `R^(') = (u^(2)sin2theta^('))/g rArr 5000 = (3464 xx 9.8 xx sin2theta)/(9.8)`
i.e. `sin2theta^(') = 5000/3464=1.44`
Which is impossible because sine of an angle cannot be more than 1. Thus this target cannot be hoped to be hit.