A boy of 50 kg mass is running with a velocity of 2 m/s. He jumps onto a stationary cart of 2kg while running. Find the velocity of cart after the boy jumps on it.
In reference to Conservation of Momentum
Answers
Answer:
m.×1= m2v2
50×=1.92m/s
Answer:
The velocity of the cart after the boy jumps on it is 1.9 m/s
Explanation:
Given :
- A boy of 50 kg mass is running with a velocity of 2 m/s.
- He jumps onto a stationary cart of 2 kg while running.
To find :
the velocity of cart after the boy jumps on it
Solution :
Momentum :
The momentum is the product of mass and velocity of the body.
Law of conservation of momentum :
The law of conservation of momentum states that the total momentum remains constant unless an external force is applied.
total initial momentum = total final momentum
Here,
total initial momentum is the sum of initial momentum if boy and initial momentum of cart.
Initial momentum of boy :
mass = 50 kg
velocity = 2 m/s
momentum = 50 × 2 = 100 kg m/s
Initial momentum of cart :
mass = 2 kg
velocity = 0 m/s (since it is at rest)
momentum = 2 × 0 = 0 kg m/s
Total initial momentum :
= 100 + 0
= 100 kg m/s
After the boy jumps onto the cart, both the boy and cart move with common velocity.
Let 'v' be the common velocity.
Final momentum :
= (mass of boy + mass of cart) × v
= (50 + 2) × v
= 52v
Applying law of conservation of momentum,
100 = 52v
v = 100/52
v ≈ 1.9 m/s