A child and a sled have a combined mass of 87.5 kg slides down a friction-less hill that is 7.34 m high. If the sled starts from rest, what is the velocity of the sled at the bottom of the hill?
V^2 = Vo^2 + 2g*h
V^2 = 0 + 19.6*7.34 = 143.864
V = 12 m/s.
To find the velocity of the sled at the bottom of the hill, we can use the principle of conservation of mechanical energy. At the top of the hill, the sled only has potential energy due to its height. As it slides down, this potential energy is converted into kinetic energy.
The equation for potential energy is given by:
PE = mgh
Where:
PE = Potential energy
m = Mass of the sled + child (combined mass)
g = Acceleration due to gravity (approximately 9.8 m/s^2)
h = Height of the hill
Given that the mass of the sled and child combined is 87.5 kg and the height of the hill is 7.34 m, we can calculate the potential energy at the top of the hill:
PE = (87.5 kg)(9.8 m/s^2)(7.34 m)
= 6417.33 Joules
According to the conservation of mechanical energy, this potential energy is converted into kinetic energy at the bottom of the hill. The equation for kinetic energy is given by:
KE = (1/2)mv^2
Where:
KE = Kinetic energy
m = Mass of the sled + child
v = Velocity of the sled
Setting the potential energy equal to the kinetic energy, we can solve for the velocity:
PE = KE
6417.33 J = (1/2)(87.5 kg)(v^2)
Simplifying the equation, we have:
12834.66 J = 43.75 kg * (v^2)
Dividing both sides by 43.75 kg, we get:
293.40448 J/kg = v^2
Taking the square root of both sides, we find:
v ≈ √293.40448 J/kg
v ≈ 17.12 m/s
Therefore, the velocity of the sled at the bottom of the hill is approximately 17.12 m/s.