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

Answer 1

Given:

Mass of the man,m

1

=80kg

Speed of man after collision, v

1

Mass of bullet m

2

=20g=0.02kg

Speed of bullet v

2

=400m/s

Acc to law of conservation of momentum

m

1

v

1

=m

2

v

2

80×v

1

=0.02×400

v

1

=

80

400×0.02

=0.1m/s

Answer 2

Question:

• A man wearing a bullet-proof vest stands still on roller skates.The total mass is 80 kg.A bullet of mass 20 grams 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?

Answer:

• The amount of velocity of the man is 0.1 metre / second

Explanation:

Given that:

• The mass of the man is 80 kilograms
• The mass of the bullet is 20 grams
• The velocity of the bullet is 400 m/s

To Find:

• What is the velocity of the man

Formula Used:

$\bigstar \; {\underline{\boxed{\bf{\frac{M_1 V_1}{T} = \frac{M_2 V_2}{T} }}}}$

Required Solution:

• According to law of conservation of momentum

★ We know that ,

${\purple{\bigstar \; \; {\boxed{\bf{ \dfrac{Mass_1 * Velocity_1}{Time} = \dfrac{Mass_2 * Velocity_2}{Time} }}}}}$

Where,

• Mass is called as the quantitative measure of inertia
• Velocity is the displacement covered by an object per unit time
• Time is the total period taken to complete the action

According to the question:

• We know that thee man wears a vest , roller skates and the bullet hits him with a force so , that means the man exerts the same amount of force as the bullet

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Derivation of formula:

★ Now according to Newton's law of motion if an object exerts some amount of force on an object the other object exerts thee same amount of force on the other object in opposite direction , now we know that

• Force = Mass × acceleration
• Force = Mass × Δ V / time

Now the formula can be written as ,

• M₁ V ₁ / t = M₂ V₂ / t

Cancelling time on both sides ,

• M₁ V₁ = M₂ V₂

Henceforth the law states that ,

• M₁ V₁ = M₂ V₂

In the case given in the question,

• Mass ₁ = 80 kg
• Mass ₂ = 20 grams
• Velocity ₂ = 400 m/s

Converting velocity ² to kilograms

• Dividing the value by 1000

$\twoheadrightarrow \sf 20 \; grams = \dfrac{20}{1000} \; kilograms$

$\twoheadrightarrow \sf 20 \; grams = 0.02 \; kilograms$

Henceforth ,

• Velocity ₂ is 0.02 kilograms ( Kg )

$\\ {\purple{\underline{\bf{\star \; Substituting \; the \; values :}}}}$  

$\longrightarrow \footnotesize \sf \dfrac{M_1 V_1}{T} = \dfrac{M_2 V_2}{T} \\ \\ \\ \longrightarrow \footnotesize \sf M_1 V_1 = M_2 V_2 \\ \\ \\ \longrightarrow \footnotesize \sf 80 \times V_1 = 0.02 \times 400 \\ \\ \\ \longrightarrow \footnotesize \sf V_1 = \dfrac{0.02 \times 400}{80} \qquad \bigg\lgroup \bf Transposing \bigg\rgroup \\ \\ \\ \longrightarrow \footnotesize \sf V_1 = \dfrac{0.02 \times 40}{8} \\ \\ \\ \longrightarrow \footnotesize \sf V_1 = 0.02 \times 5 \\ \\ \\ \longrightarrow {\footnotesize{\red{\sf{\underline{\underline{Velocity_{(of \; the \; man )} = 0.1 \; m/s }}}}}}$

Therefore:

• The velocity of the man is 01. m/s

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