Question

A little girl in Minnesota sleds down a snowy, icy hill this is 17m high. If the little girl and her sled have a combined mass of 59.0 kg, what will her kinetic energy be at the bottom of the hill? How fast will the girl be going at the bottom of the hill?

Answer 1

Kinetic energy =9839.43[J]

Velocity = 18.26[m/s]

Step-by-step explanation:

In the attached image we can see a sketch of the situation described:

In the top of the icy hill (17 m) the little girl and her sled will have the maximum potential energy with respect to the reference point (the bottom of the hill) where the elevation is zero (0).

At the bottom of the hill, all the potential energy will be transformed into kinetic energy, and she will move with me maximum velocity.

We know that because of the principle of energy transformation the potential energy will be transformed into kinetic energy.

Now resolving the equations:

`Epotential=m*g*h\\where:\\m=59[]kg]\\g=9.81[m/s^2]\\h=17[m]\\\\Ep=59*9.81*17=9839.43[J]\\`

This energy will be transformed into kinetic energy as we deducted before.

`Ek=(1)/(2) *m*v^(2) \\\\v=\sqrt{} (Ek*2)/(m)\\ v=18.26[m/s]`