Question

A player kicks a ball at a speed of $20\,ms^{-1}$ so that its horizontal range is maximum. Another player $24\,m$ away in the direction of kick starts running in the same direction at the same instant of hit. If he has to catch the ball just before it reaches the ground, he should run with a velocity equal to
(Take g $= 10\,ms^{-2}$)

• A. $2\sqrt{2}\,ms^{-1}$
• B. $4\sqrt{2}\,ms^{-1}$
• C. $6\sqrt{2}\,ms^{-1}$
• D. $10\sqrt{2}\,ms^{-1}$

Answer 1

Answer: (B)

Horizontal range, $R=\frac{u^{2}\,sin\,2\theta}{g}$
Horizontal range is maximum when angle of projection $\theta$ is $45^{°}$.
$R_{max}=\frac{u^{2}}{g}$
$=\frac{20^{2}}{10}=40\,m$
Time of flight, $T=\frac{2u\,sin\,45^{\circ}}{g}$
$=\frac{2\times20\times\frac{1}{\sqrt{2}}}{10}=2\sqrt{2}\,s$
The player can catch the ball before reaching the ground if he covers a distance
$=40=24=16\,m$ in $2\sqrt{2}\,s$.
The velocity of that player must be
$=\frac{16}{2\sqrt{2}}=4\sqrt{2}\,ms^{-1}$