A gun fires at an angle `30^@` with the horizontal and hits a target at a distance of 3 km . Can another target at a distance of 5km be hit by changing the angle of projection but keeping the velocity of projection unchanged ?

Explanation

Horizontal range ,R=`(u^2 sin 2alpha)/(g)`
In the first case, 3=`(u^2 sin(2xx30^@))/(g)=(u^2)/(g)(sqrt(3))/(2)`
or, `(u^2)/(g)=2sqrt(3)`
If the velocity of projection is unchanged, the maximum horizontal range for `alpha=45^@`, is
`R_(max)=(u^2sin(2xx45^@))/(g)=(u^2)/(g) =2 sqrt(3)`
=`2xx1.732 =3.464 km`
So, a target at a distance of 5 km cannot be hit.