Question

A player kicks a football at an angle of ${45}^{\circ }$ with a velocity of $20m{s}^{-1}$. A second player on the goal line $60m$ away in the direction of kick starts running to receive the ball at that instant. Find the speed $\left(m/s\right)$ of the second player with which he should run to strike the ball before it strikes the ground $(g=10m{s}^{-2})$

• A. $2\sqrt{2}$
• B. $\sqrt{2}$
• C. $3\sqrt{2}$
• D. $5\sqrt{2}$

Answer 1

The correct option is D $5\sqrt{2}$

Distance covered by ball in the direction of kick is equal to the range of projectile
$R=\frac{u^2\sin 2\theta }{g}=\frac{400\sin {90}^{\circ }}{10}=40m$

At the time of kick second player at a distance of $60m$ from first player. Hence distance travelled by second player to receive the ball is $20m$ and the time to cover this distance by second player should be equal to the time of flight of ball.
Assume, $x=20m$
$x=V_{2}T$ Where $V_2$ is the speed of second player and $T$ is the time of flight)
$20=V_2\times \frac{2\times 20\times \sin {45}^{\circ }}{10}$
$V_2=5\sqrt{2}m{s}^{-1}$