Question

A ball moving with a velocity v strikes a wall moving toward the ball with a velocity u. An elastic impact lasts for t sec. Then the mean elastic force acting on the ball is

• A. $\frac{2mv}{t}$
• B. $\frac{2m(\upsilon +u)}{t}$
• C. $\frac{2m(\upsilon +2u)}{t}$
• D. $\frac{m(2\upsilon +u)}{t}$

Answer 1

The correct option is B $\frac{2m(\upsilon +u)}{t}$

Relative speed of the ball $=(\upsilon +u)$
Speed after rebouncing $=-(\upsilon +u)$
Now, $F=m\frac{\Delta \upsilon }{\Delta t}=\frac{m}{t}\left[(\upsilon +u)\right]-[-\left[(\upsilon +u)\right]]$
$=\frac{2m}{t}(\upsilon +u)$