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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?
Solution
Given:
Initial speed of the ball, u = 15 m/s
The 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
\[R = \frac{u^2 \sin2\alpha}{g}\]
\[\Rightarrow R = \frac{{15}^2 \times \sin\left( 2 \times 60^\circ \right)}{9 . 8} = 19 . 88 \text{ m } \]
In the first case, the wall is 5m away from the projection point, so it is in the horizontal range of the projectile. So the ball will hit the wall. In the second case (22 m away), the wall is not within the horizontal range. So the ball would not hit the wall.
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