Question

A 400 gram soccer ball, initially at rest, is kicked. Upon contact with the ball, the foot exerts 1000 N of force, thus causing the ball to leave the foot at 30 m/s. Based on the info, how long was the foot in contact with the ball? write the formula and the process

Answer 1

Given:

A 400 gram soccer ball, initially at rest, is kicked. Upon contact with the ball, the foot exerts 1000 N of force, thus causing the ball to leave the foot at 30 m/s.

To find:

How long was the ball in contact with foot.

Calculation:

Force on an object is defined as the instantaneous rate of change of momentum of that object.

So, mathematically we can say:

$\boxed{ \sf{ \red{force = \dfrac{\Delta P}{\Delta t} }}}$

Now , putting available values in SI unit:

$= > \sf{100= \dfrac{m(v - u)}{t - 0} }$

$= > \sf{100= \dfrac{m(30 - 0)}{t - 0} }$

$= > \sf{100= \dfrac{m(30 - 0)}{t } }$

$= > \sf{100= \dfrac{30m}{t } }$

$= > \sf{100= \dfrac{30 \times \frac{400}{1000} }{t } }$

$= > \sf{100= \dfrac{30 \times 0.4}{t } }$

$= > \sf{100= \dfrac{12}{t } }$

$= > \sf{t= \dfrac{12}{100 } }$

$= > \sf{t= 0.12 \: sec }$

So, final answer is:

$\boxed{ \green{\sf{t= 0.12 \: sec }}}$