Answer to Question #92135 in Mechanics | Relativity for apon

Question

Fielder ‘F’ threw a cricket ball at a constant speed of 15 m/s and hit the stumps from a distance 30 m. The batsman ‘B’ was 15 m from the stumps and had an initial speed of 6 m/s when ‘F’ threw the ball. If ‘B’ ran with an acceleration of 1.0 m/s2, determine if ‘B’ would be ‘run out’.?

Answer 1

The time of motion of a cricket ball

$$t=\frac{S}{v}=\frac{30\:\rm{m}}{15\:\rm{m/s}}=2\:\rm{s}$$

The distance traveled by the batsman ‘B’ whithin 2 s

$$d=v_it+\frac{at^2}{2}$$

$$=6\:\rm{m/s}\times 2\:\rm{s}+\frac{1.0\:\rm{m/s^2}\times (2\:\rm{s})^2}{2}=14\:\rm{m}<15\:\rm{m}$$

Therefore, the batsman ‘B’ would be ‘run out’.