Question

A boy of mass 50 kg running at 5 m/s jumps on to a 20 kg trolley travelling in the same direction at 1.5 m/s. What is their common velocity ?

Please solve it...​

Answer 1

Answer :-

Common velocity of the boy and the trolley is 4 m/s .

Explanation :-

We have :-

→ Mass of the boy (m₁) = 50 kg

→ Velocity of the boy (u₁) = 5 m/s

→ Mass of the trolley (m₂) = 20 kg

→ Velocity of the trolley (u₂) = 1.5 m/s

To find :-

→ Their common velocity (v) .

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It is given that the boy and the trolley are travelling at the same direction .

So, their common velocity according to the 'Law of Conservation of Momentum' will be :-

m₁u₁ + m₂u₂ = (m₁ + m₂)v

⇒ 50 × 5 + 20 × 1.5 = (50 + 20)v

⇒ 250 + 30 = 70v

⇒ 280 = 70v

⇒ v = 280/70

⇒ v = 4 m/s

Answer 2

Given :-

A boy of mass 50 kg running at 5 m/s jumps on to a 20 kg trolley travelling in the same direction at 1.5 m/s.

To Find :-

Common velocity

Solution :-

At first we need to find the initial momentum of boy

p = mu

Where

p = momentum

m = mass

u = initial velocity

p = 50 × 5

p = 250 kg m/s

Now

The initial momentum of trolley

p = m'u'

Where

p = momentum

m' = mass

u' = initial velocity

p = 20 × 1.5

p = 30 kg m/s

The mass of both bodies remain same. So,

Common velocity = mu + m'u' = mv + m'v

Let the velocity be v

250 + 30 = 50(v) + 20(v)

280 = 50v + 20v

280 = 70v

280/70 = v

4 = v

Therefore

Velocity is 4 m/s