Question

A man wearing a bullet-proof vest stands on roller skates. The total mass is 80 kg. A bullet of mass 20 g is fired at 400 m/s. It is stopped by the vest and falls to the ground. What is then the velocity of the man?

(a) 1 m/s (b) 0.1 m/s

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Answer 1

$\boxed{\bf{ \red{\bigstar Find \longrightarrow }}}$

Velocity of man?

$\boxed{\bf{ \orange{\bigstar Given \longrightarrow }}}$

• mass of bullet = 20g = 0.02 kg
• mass of man = 80 kg
• initial velocity of bullet = 400 m/s
• initial velocity of man =0 m/s
• final velocity of bullet = 0 m/s

$\boxed{\bf{ \pink{\bigstar Formula \ used \longrightarrow }}}$

$\bf{m\times u+M\times U=m\times v+M\times V}$

where,

• m - mass of bullet
• M - mass of man
• u - initial velocity of bullet
• U - initial velocity of man
• v - final velocity of bullet
• V - final velocity of man

$\boxed{\bf{ \green{\bigstar SoLution \longrightarrow }}}$

Using Conservation of momentum,

put the value in the given formula , we get-

$\sf{0.02\times 400+80\times 0=0.02\times 0+80\times V}$

$\sf {V= \dfrac{0.02\times 400+ 80 \times 0}{0.02 \times 0 +80} }$

$\sf{V=\dfrac{8}{80} = 0.1}$

$\underline{\bf{\bigstar \therefore Man \ moves \ with \ a\ velocity\ of\ 0.1\ m/s \bigstar }}$

_________________________________

Answer 2

Answer:

Velocity of man?

★Given⟶

mass of bullet = 20g = 0.02 kg

mass of man = 80 kg

initial velocity of bullet = 400 m/s

initial velocity of man =0 m/s

final velocity of bullet = 0 m/s

★Formula used⟶

{m\times u+M\times U=m\times v+M\times V}m×u+M×U=m×v+M×V

where,

m - mass of bullet

M - mass of man

u - initial velocity of bullet

U - initial velocity of man

v - final velocity of bullet

V - final velocity of man

★SoLution⟶

Using Conservation of momentum,

put the value in the given formula , we get-

\sf{0.02\times 400+80\times 0=0.02\times 0+80\times V}0.02×400+80×0=0.02×0+80×V

\sf {V= \dfrac{0.02\times 400+ 80 \times 0}{0.02 \times 0 +80} }V=

0.02×0+80

0.02×400+80×0

{V=\dfrac{8}{80} = 0.1}V=

80

8

=0.1

\therefore Man \ moves \ with \ a\ velocity\ of\ 0.1\ m/s

★∴Man moves with a velocity of 0.1 m/s★

hope it helps you dear ❣️