Question

A soccer ball with a radius of $25cm$, is kicked with an initial velocity of $15m/s$ and rolls without slipping across a level horizontal grass field. If the acceleration of the ball is $-25.0\frac{m}{s^2}$
Which of the following statements best represents how many rotations the ball makes before coming to rest?

• A. $2.9$ revolutions
• B. $4.5$ revolutions
• C. $12.5$ revolutions
• D. $18$ revolutions
• E. $24$ revolutions

Answer 1

Answer: (A)

$2.9$ revolutions

Given : $v=0$ m/s $u=15$ m/s $a=-25$ $m/s^2$ $r=0.25$ m

Using $w_f^2-w_i^2=2\alpha \theta$ where $v=r{w}_f$, $u=r{w}_i$ , $a=r\alpha$

$\therefore$ $\frac{v^2}{r^2}-\frac{u^2}{r^2}=2(\frac{a}{r})\theta$

OR $0-\frac{(15{)}^2}{(0.25{)}^2}=2(\frac{-25}{0.25})\theta$ $⟹\theta =18$ radian

Thus number of revolutions $N=\frac{18}{2\pi }=2.9$ revolutions