Help with magnitude of final velocity please help!?

Question

A 0.148 kg glider is moving to the right on a frictionless, horizontal air track with a speed of 0.900 m/s. It has a head-on collision with a 0.291 kg glider that is moving to the left with a speed of 2.16 m/s. Suppose the collision is elastic.

Find the magnitude of the final velocity of the 0.148 kg glider.

Find the direction of the final velocity of the 0.148kg glider. Left or right?

Find the magnitude of the final velocity of the 0.291 kg glider.

Find the direction of the final velocity of the 0.291kg glider. Left or right?

Thanks for your help!

Answer 1

You have two issues here, first, Conservation of Momentum and second, Conservation of Energy.
Also any motion towards the left is arbitrarily negative and motion to the right, positive

Mg1= Mass Glider1
Vg1i= Initial Velocity Glider 1
Vg1f = Final Velocity Glider 1

Mg2= Mass Glider2
Vg2i= Initial Velocity Glider 2 (Note make Vg2i negative)
Vg2f = Final Velocity Glider 2

Conservation of Momentum
Mg1*Vg1i + Mg2*Vg2i= Mg1Vg1f +Mg2*Vg2f

Conservation of Energy
1/2*Mg1*(Vg1i)^2 + 1/2*Mg2*(Vg2i)^2= 1/2*Mg1(Vg1f )^2+1/2*Mg2*(Vg2f)^2

Plug all of number into the two equations above and you can solve for Vg1f and Vg2f.

(Note: Vg1f should be ~ - 3 and Vg2f ~ -2)