Question

a football kicked 20m/s at a projectile angle of 45°.a receiver on the goal line 25m away in the direction of the kick runs the same instant to meet the ball.what must be his speed,if he has to catch the ball before it hits the ground ??

Answer 1

Here is the answer......

Answer 2

Answer:

The speed of the receiver is v=5.478 m/s

Explanation:

The initial speed of the football is u=20 m/s

The angle made by the ball with the ground is $\theta=45^o$

The receiver is s= 25 m away from the starting of the projectile

The range of the projectile is $R=\dfrac{u^2 \sin 2\theta}{g}\\\\R=\dfrac{20^2 \sin 90}{9.8}\\\\R=40.81\ m$

The time of flight of the projectile is

$T=\dfrac{2u \sin \theta}{g}\\T=\dfrac{2\times 20\times \sin 45}{9.8}\\T=2.886\ s$

The distance of the end of projectile from the reciever is

d=R-s=40.81-25=15.81 m

The speed v of the receiver is

$v=\dfrac{d}{T}\\\\v=\dfrac{15.81}{2.886}\\\\v=5.478\ m/s$