A boy of mass 50kg running 5 m/s jumps on to a 20 kg trolley travelling in the same direction
at 1.5m/s . Find their common velocity
Answers
10*10²=10³7.Find area of circle whose diameter is 60 cm
Answer:
Their common velocity is 4 m/s
Explanation:
Given :
A boy of mass 50 kg running 5 m/s jumps on to a 20 kg trolley travelling in the same direction at 1.5m/s
To find :
their common velocity
Solution :
As there is no external force, the total momentum is conserved.
- The momentum of an object is defined as the product of mass and it's velocity.
- It is a vector quantity.
- SI unit : N s
Initial momentum :
It is equal to the sum of the initial momentum of boy and trolley.
Boy of mass 50kg running at 5 m/s.
m₁ = 50 kg
u₁ = 5 m/s
Trolley of mass 20 kg travelling at 1.5 m/s.
m₂ = 20 kg
u₂ = 1.5 m/s
Initial momentum = m₁u₁ + m₂u₂
➙ Initial momentum = 50(5) + 20(1.5)
➙ Initial momentum = 250 + 30
➙ Initial momentum = 280 N-s
Final momentum :
The boy jumps onto the trolley. Hence, both move with the same velocity.
Let 'v' be the common velocity.
Final momentum = m₁v + m₂v
➙ Final momentum = (m₁ + m₂)v
➙ Final momentum = (50 + 20)v
➙ Final momentum = 70v N-s
The total momentum is conserved.
Initial momentum = final momentum
280 = 70v
v = 280/70
v = 4 m/s
Therefore, their common velocity is 4 m/s