Question

A player kicks a football at an angle of ${45}^{\circ }$ with a velocity of $20m{s}^{-1}$. A second player $60m$ away along the direction of kick starts running to receive the ball at that instant. Find the speed with which second player should run to reach the ball before it hits the ground $(g=10m{s}^{-2})$

• A. $5\sqrt{2}m/s$
• B. $\sqrt{2}m/s$
• C. $3\sqrt{2}m/s$
• D. $1m/s$

Answer 1

The correct option is A $5\sqrt{2}m/s$

$R=\frac{u^2\sin 2\theta }{g}$
$R=\frac{400\times \sin {90}^{\circ }}{10}=40m$
Since the range is smaller than the distance between the second player and the first player, second player should run towards the first player.
Time required by the second player will be same as the time of flight of ball.
Distance he should run $x=60-40=20m$
$x=v\times T_f$
$x=v\times \frac{2u\sin \theta }{g}$

$20=v\times \frac{2\times 20\times \sin {45}^{\circ }}{10}$
$v=5\sqrt{2}m/s$