Q: A foot ball is kicked off with an initial speed of 19.6 m/s to have maximum range. Goal keeper standing on the goal line 67.4 m away in the direction of the kick starts running opposite to the direction of kick to meet the ball at that instant. What must his speed be if he is to catch the ball before it hits the ground ?

Sol: $\large R = \frac{u^2 sin2\theta}{g}$

$\large R = \frac{(19.6)^2 sin90^o}{9.8}$

R = 39.2 meter.

Man must run 67.4 m – 39.2 m = 28.2 m in the time taken by the ball to come to ground Time taken by the ball.

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

$\large t = \frac{2 \times 19.6 sin45^o}{9.8} = \frac{4}{\sqrt{2}}$

t = 2√2 = 2 × 1.41 = 2.82 sec.

Velocity of man $\large = \frac{28.2}{2.82} $

= 10 m/s