Question

a) 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 40 m/s. It is stopped by the vest and the man falls to th
What is then the velocity of the man? Assume there is no loss of energy.​

Answer 1

$\huge\frak{AnswEr :}$

GiveN :

• Mass of the bullet = 20 g = 0.02 kg
• Velocity of the bullet = 400 m/s
• Total mass = 80 kg

We've to calculate the velocity of the man which falls as we're given with it's mass & velocity of the bullet.

In order to calculate the velocity, Momentum is to be directly used.

Momentum maybe stated as the product of a object's mass multiplied by its velocity.

Momentum is given as :

$\because \: \large{ \boxed{ \bf{p = mv }}}$

where,

• m is the mass of the object.
• v is the velocity of the object.

So, by using this concept we'll easily find out the velocity.

Momentum of the bullet before hitting the man is,

$\longrightarrow\sf P = 0.02 \times 400$

$\longrightarrow{ \boxed{\sf P = 8 \: kgm/s}}$

Also, the after hitting the bullet, man stops & falls.

Then,

Again, by using the concept of momentum :

$\longrightarrow\sf P = mv$

$\longrightarrow\sf 8 = 80 \times v$

$\longrightarrow\sf v = \dfrac{8}{80}$

$\longrightarrow \large{ \boxed{\sf v = 0.1 m/s}}$

$\therefore$ The required velocity of the man is 0.1 m/s.