Question

A football is kicked off with an initial speed of $20m{s}^{-1}$ at a projection angle of ${45}^{\circ }$. A receiver on the goal line $60$ m away in the direction of the kick starts running to meet the ball at that instant. What must his speed be if he is to catch the ball before it hits the ground ?

• A. $3$
• B. $21$
• C. $15\sqrt{2}$
• D. $4$

Answer 1

The correct option is C $15\sqrt{2}$

The time taken by the football to land after a kick$=$Time of flight$=\frac{2u\sin \theta }{g}$

If the receiver receives the ball by running $60$m in $t$ second, his speed$=\frac{60}{t}{ms}^{-1}$

$\Rightarrow \frac{2u\sin \theta }{g}=\frac{60}{t}$

$\Rightarrow \frac{60}{t}=\frac{2\times 20\times \sin {45}^{\circ }}{g}$

$\Rightarrow t=\frac{60\times 10}{2\times 20\times \sin {45}^{\circ }}$

$\Rightarrow t=\frac{60\times 10}{2\times 20\times \frac{1}{\sqrt{2}}}$

$\Rightarrow t=\frac{600\sqrt{2}}{40}=15\sqrt{2}$seconds.