Question

A girl of mass 40kg jumps with a horizontal velocity of 5m/s on to a stationary cart with

frictionless wheel .The mass of the cart is 3kg .What is her velocity as the cart starts

moving?Assume that there is no external unbalance force working in the horizontal

direction. ​

Answer 1

Given :-

Mass of the girl = 40 kg

Mass of the cart = 3 kg

Velocity of the girl = 5 m/s

Velocity of the cart = 0 m/s

To Find :-

Velocity as the cart starts  moving.

Analysis :-

Here we are given with the mass of the girl, mass of the cart, velocity of the girl and cart.

Firstly find the momentum of the girl by substituting the values such that momentum is equal to mass multiplied by the velocity.

Then find the total mass by adding the two weight given in the question.

Substitute these two numbers we got such that velocity is equal to momentum divided by mass and find the velocity accordingly.

Solution :-

We know that,

• v = Velocity
• p = Momentum
• m = Mass

Using the formula,

$\underline{\boxed{\sf Momentum=Mass \times Velocity}}$

Given that,

Mass (m) = 40 kg

Velocity (v) = 5 m/s

Substituting their values,

⇒ p = mv

⇒ p = 40 × 5

⇒ p = 200 kg m/s

According to the question,

Momentum of girl and cart = Momentum of the girl + Momentum of cart

Substituting them,

⇒ 200 + 0 = 200 kg m/s

Finding the mass,

Total mass = m₁ + m₂

Given that,

Mass₁ = 40 kg

Mass₂ = 3 kg

Substituting their values,

⇒ m = 40 + 3

⇒ m = 43 kg

Using the formula,

$\underline{\boxed{\sf Velocity=\dfrac{Momentum}{Mass} }}$

Given that,

Momentum (p) = 200 kg m/s

Mass (m) = 43 kg

Substituting their values,

⇒ v = p/m

⇒ v = 200/43

⇒ v = 4.65 m/s

Therefore, velocity as the cart starts moving is 4.65 m/s.

Additional knowledge :-

Linear momentum:

Linear momentum is defined as the vector quantity. A body’s momentum is always in the same direction as its velocity vector.

The SI unit of linear momentum is kg m/s.

Formula: Momentum = Mass × Velocity

Where,

➡ M = Mass

➡ P = Momentum

➡ V = Velocity

Answer 2

Answer:

Given :-

• Mass of the girl = 40 kg

• Mass of the cart = 3 kg

• Velocity of the girl = 5 m/s

• Velocity of the cart = 0 m/s

To Find :-

Velocity as the cart starts moving.

Solution :-

Firstly let's find the Mounmentum of girl

[P = mv]

Here,

P = Mounmentum

M = Mass

V = Velocity

P = 40 × 5

Hence, Mounmentum of girl is 200 kg m/s .

Now,

Let's add the Mounmentum of girl and cart

200 + 0 = 200 kg m/s

$\rule{111}{10}$

Let's find total mass

Total mass = 40 + 3 = 43 kg

${\boxed {\boxed { \tt Velocity = \dfrac{Mounmentum}{Mass}}}}$

V = P/M

Velocity = 200/43

Hence :-

Velocity of cart is when start moving is 4.65 m/s.