A child leaps on a skateboard: A 35 kg girl is running at a speed of 2.8 m/s when she jumps on a stationary skateboard. If the system consisting of the girl and the skateboard begins rolling at a speed of 2.6 m/s, what is the mass of the skateboard?

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A child leaps on a skateboard: A 35 kg girl is running at a speed of 2.8 m/s when she jumps on a stationary skateboard. If the system conssting of the girl and the skateboard begins rolling at a speed of 2.6 m/s, what is the mass of the skateboard?



To answer this, we should not that momentum is conserved:

`p_i = p_f` (initial momentum is the same as the total final momentum)

Momentum is the product of mass and velocity:

`p = mv`

Initial momentum and final momentum both consists of the momentum of the girl and the skateboard. The initial momentum is:

`p_i = m_(g i r l)v_(g i r l) + m_(b o a r d)v_(b o a r d)`

`p_i = 2.8*35 + m_(b o a r d)*0 = 98 + 0 = 98N`

The skateboard doesn't have a momentum because it is at rest. The final momentum is caused by the new system, a girl on the skateboard. Hence,

`p_f = m_(g i r l - o n - b o a r d)v_(g i r l - o n - b o a r d)`

Note that the mass would be the total mass of the girl and the skateboard:

`p_f = (m_(b o a r d) + 35)*2.6 = 2.6*m_(b o a r d) + 91`

Since momentum is conserved, this is just equal to 98N, the initial momentum:

`2.6*m + 91 = 98`

`2.6*m = 98 - 91`

`2.6*m = 7`

`m = 2.69 kg`

Hence, the skateboard is 2.69 kilograms.

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