Question

During the RCB vs CSK match, while batting Virat kohli edges a ball vertically with a velocity of 30ms-1. Dhoni standing behind the stumps runs to catch it. If he is standing 3 m behind the stumps and runs at 0.5ms-1 will he be able to catch the ball? (g=10ms-2)

Answer 1

We consider vertical motion of the ball, where,

• vertical velocity of the ball $\sf{=30\ m\,s^{-1}.}$

We consider upward motion as positive.

• acceleration acting on the ball $\sf{=-g=-10\ m\,s^{-2}.}$

Let the ball come back to the ground after a time $\sf{t}$ seconds of rising up.

On coming back to the ground, the ball attains a zero vertical displacement. Hence by second equation of motion,

$\longrightarrow\sf{s=ut+\dfrac{1}{2}\,at^2}$

$\longrightarrow\sf{0=30t-5t^2}$

$\longrightarrow\sf{5t(t-6)=0}$

Since $\sf{t\neq0,}$

$\longrightarrow\sf{t=6\ s}$

So the ball should reach the ground after 6 seconds. This time should be taken by Dhoni too, as minimum, to catch the ball.

Now we have to check whether Dhoni should reach there to catch the ball, by covering the distance of 3 m in 6 seconds or not.

• Displacement to be covered by Dhoni $\sf{=3\ m.}$

• Dhoni's speed $\sf{=0.5\ m\,s^{-1}.}$

• Dhoni experiences no acceleration.

Hence, by second equation of motion,

$\longrightarrow\sf{s=ut+\dfrac{1}{2}\,at^2}$

$\longrightarrow\sf{3=0.5t}$

$\longrightarrow\sf{t=6\ s}$

Therefore, Dhoni will be able to catch the ball!

Answer 2

Answer:

Please refer to the attached document...