Question

2 ptsAlly, Brittany, Christine, and Danica are exercising on the track field. Their masses are55 kg, 60 kg, 50 kg, and 55 kg, respectively. Ally and Christine are walking around thetrack together at the same speed. Danica is running around the track, and Brittany hasstopped to tie her shoe. Rank the girls from least to greatest momentum.

Answer 1

`\text{Brittany, Christine, Ally, Danica}`

Step-by-step explanation

To solve this problem, we have to find the momentum of each of the girls.

Momentum can be found by applying the formula:

`p=mv`

where m = mass; v = velocity

Let the velocity of the person running be x.

Let the velocity of the person walking be y.

Let the velocity of the person tying her shoe be z.

The person running is moving at a much higher velocity than the person walking while the person tying her shoe is not moving at all i.e. z = 0

Therefore, we have that:

`x>y>z`

Let us calculate the momentum of each girl:

`\begin{gathered} p_{\text{Ally}}=55\cdot y=55y\text{ kgm/s} \\ p_{\text{Brittany}}=60\cdot z=60\cdot0=0\text{ kgm/s} \\ p_{\text{Christine}}=50\cdot y=50y\text{ kgm/s} \\ p_{\text{Danica}}=55\cdot x=55x\text{ kgm/s} \end{gathered}`

Therefore, knowing that x > y, we have that the ranking of the momentum from least to greatest is:

`0,50y,55y,55x`

Therefore, the ranking of the girls from least to greatest momentum is:

`\text{Brittany, Christine, Ally, Danica}`