Question

A foot-ball player hits the ball with speed 20 m s⁻¹ with angle 30° with respect to horizontal direction as shown in the figure. The goal post is at distance of 40 m from him. Find out whether ball reaches the goal post?

Answer 1

Final Answer : Ball will not reach the Goal Post directly, but However if we are considering the bouncing of ball on the ground then it may reach.


Steps :
1) We have,
Initial velocity, u = 20m/s
Angle made by Horizontal, theta = 30°.
acceleration due to gravity, g = 10m/s^2

2)
Here,
Range is given by :
$\frac{ {u}^{2} \sin( 2\theta) }{g} = \frac{ {20}^{2} \times \sin(60 \degree) }{10} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 20 \sqrt{3} = 34.64 \: m \div s$


3) Hence, we observe that
Range < 40 m (distance from goal post)
Therefore, Ball will not reach the goal post DIRECTLY.

PRACTICALLY, IT MAY REACH THE GOAL POST BY BOUNCING ON THE GROUND.

Answer 2

If the ball is to reach the goal post, the range of the ball must be equal to the distance between the goal post and the player.
Speed = 20ms⁻¹ = u
Angle = 30° = α
g = 9.8ms⁻²
Horizontal range of a projectile = [u²×sin(2α)]/g = 20×20×√3/2/9.8 = 35.34m
As range is less than 40m, the ball will not reach the goal post in the first attempt. It can reach the goal after bouncing.