Question

A child and a sled with a combined mass of 50.0 kg slide down a frictionless hill. If the sled starts from rest and has a speed of 9.0 m/s at the bottom, what is the height of the hill?

Answer 1

297.38 meters

Step-by-step explanation:

The height of the hill can be calculated using the principle of conservation of energy. This principle states that the total energy of a system is conserved, and that the change in potential energy of an object is equal to the work done on it.


The height of the hill can be calculated using the formula:

h = (1/2) m v^2 / g

where m is the mass of the child and sled, v is the final speed of the sled, and g is the acceleration due to gravity (9.8 m/s^2).

Plugging in the values, we get:

h = (1/2) * 50.0 kg * (9.0 m/s)^2 / 9.8 m/s^2

h = (1/2) * 50.0 kg * 81.0 m^2/s^2 / 9.8 m/s^2

h = 40.5 kg * 81.0 m^2/s^2 / 9.8 m/s^2

h = 2911.76 kg m^2/s^2 / 9.8 m/s^2

h = 297.38 m

So the height of the hill is 297.38 meters.