Question

A ball is projected from a point on the floor with a speed of 15 m/s at an angle of 60° with the horizontal. Will it hit a vertical wall 5 m away from the point of projection and perpendicular to the plane of projection without hitting the floor? Will the answer differ if the wall is 22 m away?

Answer 1

Given:
Initial speed of the ball, u = 15 m/s
Angle of projection with horizontal, α = 60°
Distance of the wall from the point of projection = 5 m
a = g = 9.8 m/s² (Acceleration due to gravity)
We know that the horizontal range for a projectile is given by
$R=\frac{u^2\sin 2\alpha }{g}$
$\Rightarrow R=\frac{{15}^2\times \sin \left(2\times 60°\right)}{9.8}=19.88\mathrm{m}$
As the horizontal range of the projectile is 19.88 m, the ball will hit the wall 5 m away from the point of projection. If the wall is 22 m away from the point of projection, the ball will hit the wall because it is not in its horizontal range.