Question

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

Answer 1

Explanation:

boy

Mass = 50kg

Velocity = 5m/s

trolley

Mass = 20 kg

Velocity = 1.5 m/s

so using conservation law of momentum

MV + mv = ( M + m ) v'

50*5 + 20*1.5 = ( 50 + 20 ) v'

250 + 30 = 70 v'

280 = 70 v'

so v' = 4m/s which is their common velocity.

Answer 2

Answer:-

• Common Velocity = $\bf{4 \: m/s}$

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• Given:-

Mass of boy [M] =$\bf{50 \: kg}$

Velocity of the boy [V] =$\bf{5 \: m/s}$

Mass of the Trolley [m] =$\bf{20 \: kg}$

Velocity of the Trolley [v] =$\bf{1.5 \: m/s}$

• To Find:-

Common Velocity =$\bf{?}$

• Solution:-

We know,

Conservative Law of Momentum:-

$\boxed{MV + mv = [M + m]v'}$

here,

$\bf{M}$ = Mass of the boy

$\bf{V}$ = Velocity of the boy

$\bf{m}$ = Mass of the Trolley

$\bf{v}$ = Velocity of the Trolley

$\bf{v'}$ = Common Velocity

Hence,

$\implies$50 × 5 + 20 × 1.5 = [50 + 20]v'

$\implies$250 + 30 = 70 v'

$\implies$280 = 70 v'

$\implies$v' = $\dfrac{280}{70}$

$\implies\bf{v' = 4 \: m/s}$

Therefore,

Common Velocity [v'] is $\bf{4 \: m/s}$

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