Part e a small toy cart equipped with a spring bumper rolls toward a wall with a speed of v. the cart rebounds from the wall, with the same speed v. the sketch below shows the initial velocity vector v⃗ i, final velocity vector v⃗ f, and the initial momentum vector p⃗ i. using the initial momentum vector as a basis, draw the change in momentum vector δp⃗ for the cart. you can obtain each vector's length and orientation by clicking on it to select it.

Δp = -2 p₀

Explanation:

The momentum is defined by

         p = m v

In this case we write the initial and final momentum, we take as positive the direction towards the wall.

         p₀ = m v

         p_f = m (-v)

the negative sign is because the car is bouncing off the wall

the change of the moment is

       Δp = p_f - p₀

        Δp = - m v - m v

        Δp = -2 mv

        Δp = -2 p₀

we see that the change of moment is twice the moment, in the attachment we can see the vectors of these changes and the sign indicates the direction of the change at the moment

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.