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

$24m{s}^{-1}$

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B

$35m{s}^{-1}$

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C

$12m{s}^{-1}$

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D

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

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Solution

The correct option is D $46m{s}^{-1}$Step 1: Given dataForce, $F=1200N$Mass of ball, $m=0.5kg$Time, $∆t=25ms$Initial velocity, $u=14m/s$Step 2: Find final speed of the steel ball$\begin{array}{rcl}F& =& \Delta p/\Delta t\\ F\left(\Delta t\right)& =& \Delta p\\ –1200x25x{10}^{-3}& =& {P}_{2}–{P}_{1}\\ –1200x25x{10}^{-3}& =& -mv-mu\\ 1200x25x{10}^{-3}& =& \left(1/2\right)v+\left(1/2\right)u\\ 2x1200x25x{10}^{-3}& =& v+u\\ 2x1200x25x{10}^{-3}& =& v+14\\ v& =& 60–14\\ v& =& 46m/s\end{array}$Hence, option D is correct.

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