Two carts on an air track undergo a head‐on perfectly elastic collision. the first cart, with 0.060 kg mass, is initially moving in the +x direction with speed 4.5 m/s. the second cart, with mass 0.090 kg is also moving in the +x direction, but with a speed of 3.0 m/s. calculate the speed and direction of each cart following the collision.

The final speed of cart with mass 0.06 kg is 2.7 m/s and the final speed of the cart of mass 0.09 kg is 4.2 m/s.

Explanation:

Initial moumentum of cart with mass 0.06 kg is

Initial moumentum of cart with mass 0.06 kg is

Thus initial moumentum of system is

Now let the final velocity of 0.06 kg cart be and that of 0.09 kg cart be

Thus final moumentum of system is

Equating initial and final values we get

Similarly conserving the kinetic energies of the 2 carts we get

Solving equation i and ii we get

Substituting value of from i and using it in equation ii we get

Solving for we get

Similarly

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