Toy Car Elastic Collision, finding speed and velocity?

Question

A 35 G toy car going right at 5 m/s has an elastic head on collision with a 30 g toy car going left at 3 m/s. After the collision, what are their velocities? (Speed and Direction)? ANy help would be useful. I set up 2 equations and used a substitution mehoid to solve but have no clue if i'm right. These equations were: A) A) 35( 5 ) - 30( 3 ) = 35V + 30(V2) and B ) 1/2 (35)( 5 )^2 - 1/2(30)( 3 )^2 = 1/2(35)( V )^2 + 1/2(30)(V2)^2

Answer 1

Equation A is correct since momentum is a vector quantity it has direction.

kinetic energy in equation B is scalar, so you should not subtract.

I got the quadratic equation:

75.83*V1^2-198.3*V1-904.167=0

Which gives two roots
V1=5, or -2.384
the negative is the one I chose since the collision must be elastic and there is only one direction of motion (either positive or negative right or left).

Given this, I computed
V1=-2.384
V2=5.6

j

Answer 2

as a results of fact the collision is inelastic, the fee after the collision is given by using the finished momentum earlier the collision divided by using the finished mass. So if m,m' are the hundreds and u,u' are the velocities then the final velocity is (mu+m'u')/(m+m'). in this difficulty m = 0.4, m' = 0.3, u = 0.a million and u' = 0 so the final velocity is (0.4x0.a million)/0.7 = 0.057...m/s. to locate the shortcoming of KE, word that the toy vehicle has no KE earlier impact so the KE earlier impact is (0.5)x(0.4)x[(0.a million)^2]=0.002 and after impact we've a 0.7kg mass shifting at 0.057...m/s so the KE is (0.5)x (0.7)x (0.057...)^2 = 0.0011429 and the loss is 0.000857... instruments. word that there is an invaluable formula for the shortcoming of KE in a collision. it fairly is (a million/2)mm' (a million-e^2)[(u-u' )^2]/(m+m' ), the place e is the coefficient of restitution it is 0 for an inelastic collision. for that reason for an inelastic collision, the shortcoming of KE is given by using (a million/2)mm' [(u-u' )]^2/(m+m' ). in case you replace the values into this expression you will arrive on the comparable answer as given above.