Question

A bullet of mass $10$ g moving with speed $600$ m/s strikes a sand bag of mass $10$ kg moving on a frictionless surface with speed $0.5$ m/s in opposite direction. If bullet gets embedded in the bag, then velocity of combined (sand bag $+$ bullet) will be nearly.

Answer 1

Mass of bullet should be $=10gm=0.01kg$

initial velocity (U)of bullet$=1000m/s$

final velocity$\left(V\right)=0m/s$(because it has stopped after striking sand)

displacement of bullet$=5cm=0.05m$

a)using $2as=V²-U²$

$2\left(a\right)\left(0.05\right)=0²-1000²$

$2a\left(5/100\right)=-1000000$

$2a\left(1/20\right)=-1000000$

$a\left(1/10\right)=-1000000$

$a=-10000000=-{10}^7$

acceleration of bullet is $-{10}^{7}or-10000000$

by using$F=ma$

$F=0.01\left(10000000\right)$

$F=1/100\left(10000000\right)$

$F=-100000N$

there fore resistive force of bullet$=-100000N$

b)by using $a=v-u/t$

$-10000000=0-1000/t$

$-10000000=-1000/t$

$-10000=t$

or

$t=-10⁴seconds$