What will be the magnitude of recoil speed of a tank which weighs 0.4 tonnes and fires a projectile of mass 3 kg with a velocity of 24 m/s?

Question

Question

Answer 1

CONCEPT:

Momentum: Momentum is the product of the mass and the velocity of an object or particle. It is a vector quantity.
- The standard unit of momentum magnitude is the kilogram-meter per second (kg·m/s).

P = m v

Where P = momentum, m = mass of the body, v = velocity of body.

Conservation of Linear Momentum: Conservation of Linear Momentum states that a body in motion retains its total momentum (product of mass and vector velocity) unless an external force is applied to it.
In mathematical term

Initial momentum = Final momentum

P₁= P₂

We can say that

M₁V₁ + M₂V₂= 0

Where M₁ = mass of projectile, V₁ = velocity of projectile, M₂ = mass of tank and V₂ = Unknown recoil speed of tank

CALCULATION:

Given that M₁ = 3 kg, V₁= 24 m/s, M₂ = 0.4 tonnes = 400 kg

Substituting these values in the formula:

M₁V₁ + M₂V₂= 0

(3 × 24) + (400 × V₂) = 0

V₂ = -0.18 m/s,

The tank recoils in the backward direction with a magnitude of 0.18 m/s.

So option 2 is correct.