Question

A player kicks a football obliquely at a speed of $20m/s$ so that it's range is maximum. Another player at a distance of $24m$ away in the direction of kick, starts running at that instant to catch the ball. The constant speed with which he has to run is $(g=10m{s}^{-2})$

• A. $4m{s}^{-1}$
• B. $4\sqrt{2}m{s}^{-1}$
• C. $8\sqrt{2}m{s}^{-1}$
• D. $8m{s}^{-1}$

Answer 1

The correct option is B $4\sqrt{2}m{s}^{-1}$

$R_{max}=\frac{u^2\sin 2\theta }{g}$ for $R_{max}\Rightarrow \theta ={45}^0$
$R_{max}=\frac{u^2}{g}$
$u=20m/s$
$R=40m$
$t_f=\frac{2u\sin \theta }{g}=\frac{2\times 20\times \frac{1}{\sqrt{2}}}{10}=2\sqrt{2}s$

Boy has to cover $40-24=16m$ in $2\sqrt{2}s$

So his speed should be $=\frac{16}{2\sqrt{2}}=4\sqrt{2}m/s$