Question

A force of $1200N$ acts on a $0.5kg$ steel ball as a result of a collision lasting $25ms$. If the force is in a direction opposite to the initial velocity of $14m{s}^{-1}$, then the final speed of the steel ball would be

• A. $24m{s}^{-1}$
• B. $35m{s}^{-1}$
• C. $12m{s}^{-1}$
• D. $46m{s}^{-1}$

Answer 1

The correct option is D

$46m{s}^{-1}$

Step 1: Given data

Force, $F=1200N$

Mass of ball, $m=0.5kg$

Time, $∆t=25ms$

Initial velocity, $u=14m/s$

Step 2: Find final speed of the steel ball

$\begin{array}{rcl}F& =& \Delta p/\Delta t\\ F\left(\Delta t\right)& =& \Delta p\\ –1200x25x{10}^{-3}& =& P_2–P_1\\ –1200x25x{10}^{-3}& =& -mv-mu\\ 1200x25x{10}^{-3}& =& (1/2)v+(1/2)u\\ 2x1200x25x{10}^{-3}& =& v+u\\ 2x1200x25x{10}^{-3}& =& v+14\\ v& =& 60–14\\ v& =& 46m/s\end{array}$

Hence, option D is correct.