Question

A player kicks a football of mass $0.5kg$ and the football begins to move with a velocity of $10m/s$. If the contact between the leg and the football lasts for $1/50s,$then the force acted on the ball should be

• A. $2500N$
• B. $1250N$
• C. $250N$
• D. $625N$

Answer 1

The correct option is C

$250N$

Step 1: Given data

Mass of the football, $m=0.5Kg$

Initial velocity of football, $u=0m/s$ [As, football was initially at rest]

Final velocity of football, $v=10m/s$

Time of contact between leg and football, $t=1/50s$

Step 2: Find the change in momentum, $\mathbf{∆}\mathit{P}$

change in momentum, $∆P=mv-mu$

$$\begin{gathered} =0.5\times 10-0.5\times 0 \\ =5-0 \\ =5Kg.m/s \end{gathered}$$

Step 3: Find the force acted on the ball, $\mathit{F}$

Force on the ball, $F=∆P/t$ [From the Newton's second law of motion]

$$\begin{gathered} =5/(1/50) \\ =250N \end{gathered}$$

Hence, option (C) is correct.