A bullet of mass $20 \mathrm{~g}$ moving with a velocity of $200 \mathrm{~m} / \mathrm{s}$ strikes a target…
A bullet of mass $20 \mathrm{~g}$ moving with a velocity of $200 \mathrm{~m} / \mathrm{s}$ strikes a target and is
brought to rest in $\left(\frac{1}{50}\right)^{\text {th }}$ of a second. The impulse and average force of impact are respectively
$2 \mathrm{Ns}, 100 \mathrm{~N}$
$4 \mathrm{Ns}, 100 \mathrm{~N}$
$2 \mathrm{Ns}, 200 \mathrm{~N}$
$4 \mathrm{Ns}, 200 \mathrm{~N}$
Solution
When a bullet of mass $m$ moving with a velocity $v$ strikes a target and is brought to rest in time $t$, the impulse $J$ and average force $F_{\text {avg }}$ are calculated using the following relations:
1. Impulse is the change in momentum:
$J=\Delta p=m \times v$
2. Average force is given by the impulse divided by time:
$F_{\mathrm{avg}}=\frac{J}{t}=\frac{m \times v}{t}$
Given the correct values from the options, Answer (4) is correct.