A child and sled with a combined mass of 45.0 kg slide down a frictionless hill. If the sled starts from rest and has a speed of 8.0 m/s at the bottom, what is the height of the hill (include units)?
since the p.e at the top of the hill was converted to k.e at the bottom:v^2=2gh 8^2=2*10h 64=20h h=3.2m
To find the height of the hill, we can use the principle of conservation of energy. At the top of the hill, the sled and child have only gravitational potential energy. At the bottom of the hill, all of this energy is converted into kinetic energy.
The gravitational potential energy (PE) can be calculated using the formula:
PE = m * g * h
where m is the mass (combined mass of the sled and child) and g is the acceleration due to gravity (9.8 m/s²).
At the bottom of the hill, all the potential energy is converted into kinetic energy (KE):
KE = (1/2) * m * v^2
where v is the final velocity (8.0 m/s).
Setting the potential energy equal to the kinetic energy, we have:
m * g * h = (1/2) * m * v^2
We can cancel out the mass from both sides of the equation:
g * h = (1/2) * v^2
Now, solving for the height (h):
h = (1/2) * v^2 / g
Substituting the known values, we have:
h = (1/2) * (8.0 m/s)^2 / 9.8 m/s²
h = (1/2) * 64.0 m²/s² / 9.8 m/s²
h = 32.0 m²/s² / 9.8 m/s²
h ≈ 3.27 meters
Therefore, the height of the hill is approximately 3.27 meters.