$3.$ For this problem, suppose you have a mass of $70$ kg and you have a $7-$year old niece of mass $20$ kg $.$ You are at the playground and your niece wants to compete with you to see who can be faster on the swings. The seats of the swings are $0\mathrm{.}8$ m above the ground and are connected with a rope of length $3$ m to the bar above. Suppose your niece's center of mass is $0\mathrm{.}1$ m above the seat and your center of mass is $0\mathrm{.}3$ m above the seat. At most, your niece's center of mass ascends $2$ m from its starting height, whereas your center of mass ascends only $1\mathrm{.}5$ m above its starting height.

A$)$ Calculate your niece's maximum speed on the swing.

B$)$ Calculate an estimate for how long it takes you to complete ten swings.

C$)$ Considering your analyses in both parts A and B $($and any other necessary calculations$),$ explain who, if either of you, was faster on the swings.