Question

A girl of mass 40 kg jumps with a horizontal velocity of 5m/s onto a cart with frictionless wheels. The mass of the cart is 3kg. What is her velocity as the cart starts moving? Assume that there is no external unbalanced force working in horizontal direction.

Answer 1

Hey Pretty Stranger!

Let v be the velocity of the girl on the cart as the cart starts moving.

The total momenta of the girl and cart before the interaction

→ 40 kg × 5 m/s + 3 kg × 0 m/s

→ 200 kg m/s + 0 m/s

→ 200 kg m/s

Total momenta after the interaction :

→ (40 + 3) kg × v m/s

→ 43 v kg m/s

According to law of conservation of Momentum :

→ 43v = 200

→ v = $\sf \: \dfrac{200}{43}$

→ v = 4.65 m/s

$\therefore$ The girl on cart would move with a velocity of 4.65 m/s in the direction in which the girl jumped.

Answer 2

Answer:

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

Let's find total mass

Total mass = 40 + 3 = 43 kg

Velocity=Mounmentum/mass

V = P/M

Velocity = 200/43

Hence :-

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

@ananya