Question

A green croquet ball of mass 0.50 kg is rolling at +12 m/s. It collides with a blue croquet ball that also

has a mass of 0.50 kg, it is initially at rest.

a. If the green ball continues moving forward with a velocity of +2.4 m/s, what is the final velocity
of the blue croquet ball?


b. If the green ball continues moving forward with a velocity of +0.30 m/s, what is the final
velocity of the blue croquet ball?


c. If the green ball comes to a stop after the collision, what would the final velocity of the blue
croquet ball be?


(PLEASE HELP MY QUESTIONS ARE DUE BY 4:00 and I was not taught Any of the questions I’ve asked!)

Answer 1

a) 9.6 m/s

b) 11.7 m/s

c) 12 m/s

Step-by-step explanation:

This problem can be solved by the Conservation of Momentum principle, which establishes that the initial momentum
`p_(o)` must be equal to the final momentum
`p_(f)`:

`p_(o)=p_(f)` (1)

Where:

`p_(o)=m_(g) V_(o) + m_(b) U_(o)` (2)

`p_(f)=m_(g) V_(f) + m_(b) U_(f)` (3)

`m_(g)=0.5 kg` is the mass of green ball

`m_(b)=0.5 kg` is the mass of the blue ball

`V_(o)=12 m/s` is the initial velocity of the green ball

`U_(o)=0 m/s` is the initial velocity of the blue ball

`V_(f)` is the final velocity of the green ball

`U_(f)` is the final velocity of the blue ball

Substituting (2) and (3) in (1):

`m_(g) V_(o) + m_(b) U_(o)=m_(g) V_(f) + m_(b) U_(f)` (4)

Isolating
`U_(f)`:

`U_(f)=(m_(g) V_(o)  - m_(g) V_(f))/(m_(b))` (5)

`U_(f)=(m_(g) (V_(o)  - V_(f)))/(m_(b))` (6) This is the equation we will use for the next cases

Knowing this, let's begin with the answers:

a) In this case
`V_(f)=2.4 m/s` and we have to find
`U_(f)`

`U_(f)=(0.5 kg (12 m/s  - 2.4 m/s))/(0.5 kg)` (7)

`U_(f)=9.6 m/s` (8)

b) In this case
`V_(f)=0.3 m/s` and we have to find
`U_(f)`

`U_(f)=(0.5 kg (12 m/s  - 0.3 m/s))/(0.5 kg)` (9)

`U_(f)=11.7 m/s` (10)

c) In this case
`V_(f)=0 m/s` and we have to find
`U_(f)`

`U_(f)=(0.5 kg (12 m/s  - 0 m/s))/(0.5 kg)` (11)

`U_(f)=12 m/s` (12)