A boy of mass 50kg running at 5m/s jums on to a 20kg trolly travelling in the same direction at 1.5m/s .what is their common velocity.
4m/s
correct.
To find the common velocity of the boy and the trolley, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the boy jumps onto the trolley is equal to the total momentum after the boy jumps.
The momentum of an object is calculated by multiplying its mass by its velocity. If we consider the positive direction of motion to be in the same direction as the boy and the trolley (i.e., to the right), then we can write the equation for the conservation of momentum as:
(mass of boy × velocity of boy) + (mass of trolley × velocity of trolley) = (mass of boy + mass of trolley) × common velocity
Substituting the values given in the question:
(50 kg × 5 m/s) + (20 kg × 1.5 m/s) = (50 kg + 20 kg) × common velocity
Simplifying the equation:
(250 kg⋅m/s) + (30 kg⋅m/s) = (70 kg) × common velocity
280 kg⋅m/s = 70 kg × common velocity
We can now solve for the common velocity by dividing both sides of the equation by 70 kg:
common velocity = (280 kg⋅m/s) ÷ (70 kg)
common velocity = 4 m/s
Therefore, the common velocity of the boy and the trolley after the boy jumps onto it is 4 m/s.