Question

A soccer ball is kicked from the ground with an initial speed of 20 m/s at an upward angle of ${45}^{\circ }$. A player 55 m away in the direction of the kick starts running to meet the ball at that instant. What must be his average speed if he is to meet the ball just before it hits the ground?

• A. (4 - 5) m/s
• B. (5 - 6) m/s
• C. (6 - 7) m/s
• D. (3 - 4) m/s

Answer 1

The correct option is B

(5 - 6) m/s

R = $\frac{u^{2}sin2\theta }{g}$
$\theta$ = ${45}^{\circ }$
R = $\frac{(20{)}^{2}sin{90}^{\circ }}{10}$
= $\frac{400}{10}$
R = 40m
T = $\frac{2usin\theta }{g}$ = $\frac{2\times 20\times sin{45}^{\circ }}{10}$
= $\frac{4}{\sqrt{2}}$= $\frac{4}{1.414}$ = 2.8s Approx

Now distance to be covered by player = 55 - 40 = 15m
T = 2.8s Average speed = $\frac{D}{t}$ = $\frac{15}{2.8}$ = 5.35 $\frac{m}{s}$ approx