Question

Aditi of mass 50 kg jumps with a horizontal velocity of 5 m/s onto

a boat. The mass of the boat is 5 kg. What is her velocity as the boat starts moving?

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Answer 1

Answer :-

4.54m/s

Explanation :-

Given :

Mass of Aditi,m_1 = 50kg

Initial velocity of Aditi,u_1 = 5m/s

Mass of the boat,m_2 = 5kg

Initial velocity of the boat,u_2 = 0m/s (As it was in rest)

Let the final velocity of (Aditi & Car) = v

To Find :

Final velocity,v = ?

Solution :

According to the conservation law of momentum,

$\sf{}m_1u_1+m_2u_2=m_1v_1+m_2v_2$

Put their values and find “v”

$\sf{}\implies 50kg\times 5m/s+5kg\times 0=50kg\times v+5kg\times v$

$\sf{}\implies 250kg\ m/s=50kg\times v+5kg\times v$

$\sf{}\implies 250kg\ m/s=(50kg+5kg)v$

$\sf{}\implies 250kg\ m/s=55kg\times v$

$\sf{}\implies \dfrac{250kg\ m/s}{55kg}= v$

$\sf{}\therefore v= 4.54m/s$

Therefore,velocity of Aditi after the boat start moving is equal to 4.54m/s