Describe the steps in solving the problem below. A red cart of mass 4 kg slides to the right on a frictionless track with a velocity of +4 m/s. It collides with the stationary blue cart of mass 1 kg. After the collision, the blue cart has a velocity of +8 m/s. Calculate the velocity of the red cart after the collision.

Afaulty model rocket moves in the xy-plane (the positive y direction is vertically upward). the rocket's acceleration has components ax(t) = ? t2 and ay(t) = ? ? ? t, where ? = 2.50 m/s4 , ? = 9.00 m/s2 , and ? = 1.40 m/s3 . at t = 0 the rocket is at the origin and has velocity ~v0 = v0x ? i + v0y ? j with v0x = 1.00 m/s and v0y = 7.00 m/s. (a) calculate the velocity and position vectors as functions of time. (b) what is the maximum height reached by the rocket? (c) sketch the path of the rocket. (d) what is the horizontal displacement of the rocket when it returns to y = 0?