a body B moving a velocity of 20m/s collid with anothet body A moving in the same direction on the same horzontal line with a velocity of 10m/s, if the of body A is three time the same of body B and the collion perfectly elastic calculate the velocity of A and aftet the collision, calculate the velocity of B telative to that of A after the collisul

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To answer this question, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

Let's denote the mass of body A as Ma, and the mass of body B as Mb. Given that the mass of body A is three times that of body B (Ma = 3Mb), we can substitute this information into our calculations.

1. Calculate the initial momentum:
Momentum (p) = mass (m) * velocity (v)
Initially, the momentum of body A (pa) is Ma * 10 m/s
The momentum of body B (pb) is Mb * 20 m/s

2. Determine the total initial momentum:
Total initial momentum (pi) = pa + pb

3. Apply the principle of conservation of momentum:
According to conservation of momentum, the total initial momentum is equal to the total final momentum.
So, pi = total final momentum

4. Analyze the collision:
In a perfectly elastic collision, the total kinetic energy before and after the collision remains the same. Additionally, the relative velocities of the bodies after the collision can be determined using the following formula:
Relative velocity (Vrel) = (Velocity of B - Velocity of A)

5. Calculate the velocity of A after the collision:
Since the collision is perfectly elastic, we can use the momentum conservation principle to solve for the velocity of A after the collision.

Final momentum of body A (pa') = Ma * velocity of A after collision
Final momentum of body B (pb') = Mb * velocity of B after collision

6. Apply the principle of conservation of momentum:
pi = pa' + pb'

7. Calculate the velocity of B relative to A after the collision:
Use the relative velocity formula mentioned earlier to find the velocity of B relative to A after the collision.

Now, let's perform the calculations using the given values:
Ma = 3Mb
Velocity of A = 10 m/s
Velocity of B = 20 m/s

1. Calculate the initial momentum:
pa = Ma * 10 m/s = 3Mb * 10 m/s = 30Mb m/s
pb = Mb * 20 m/s

2. Determine the total initial momentum:
pi = pa + pb = 30Mb m/s + Mb * 20 m/s = 50Mb m/s

3. Apply the principle of conservation of momentum:
pi = pa' + pb'
50Mb m/s = Ma * velocity of A after collision + Mb * velocity of B after collision

4. Calculate the velocity of A after the collision:
Since body A and body B have the same mass ratio as their initial velocities (10 m/s and 20 m/s), they will exchange velocities after the collision.
Velocity of A after collision = 20 m/s
Velocity of B after collision = 10 m/s

5. Apply the principle of conservation of momentum:
50Mb m/s = 3Mb * 20 m/s + Mb * 10 m/s
50Mb m/s = 60Mb m/s + 10Mb m/s

6. Calculate the velocity of B relative to A after the collision:
Vrel = Velocity of B - Velocity of A
Vrel = 10 m/s - 20 m/s
Vrel = -10 m/s

So, the velocity of body A after the collision is 20 m/s, and the velocity of body B relative to A after the collision is -10 m/s.