Question

Cart 1 of mass m is traveling with speed 2, v, start subscript, 0, end subscript in the+ x plus, x-direction when it has an elastic collision with cart 2 of mass 2m traveling with speed​ v, start subscript, 0, end subscript in the same direction.

Answer 1

Your question was incomplete hence I am writing down the complete version of the question below.

Q) Cart-1 of mass m is travelling with a speed of v0 in +x direction when it has an elastic collision with Cart-2 of mass 2m travelling with a speed of v0 in –x direction.What are the velocities of cart after collision?

Answer:

V1f = -5Vo3

V2f = Vo/3

Step-by-step explanation:

Let us assume the mass of cart-1 as m1 and mass of cart-2 as m2, now we know that mass of cart-1 is m and cart-2 is 2m hence,

m1 = m

m2 = 2m

let the initial velocity of cart-1 be µ1 = Vo and the initial velocity of cart-2 µ2 = -Vo and the final velocity of cart-1 be V1f and the final velocity of cart-2 be V2f

Now we will apply the conservation of momentum formula for the case given,

m1µ1 + m2µ = m1V1f + m2V2f

substituting the values in above equation we get,

mVo - 2mVo = mV1f + 2mV2f

-mVo = m( V1f + 2V2f)

V1f + 2V2f = -Vo ----------------------(1)

Now we know that the value of e for elastic collision is 1 hence,

V2f -V1f = µ1 -µ2 = Vo -( -Vo)

V2f - V1f = 2Vo--------------------(2)

Adding equation (1) and (2) we get,

3V2f = Vo

V2f = Vo/3

Subsituting the value of V2f in equation (2)

V1f = V2f -2Vo = Vo/3 - 2Vo

V1f = -5Vo/3