Question

A child and sled with a combined mass of 54 kg slide down a frictionless hill that is 6.9 m high. If the sled starts from rest, how much kinetic energy will they have at the bottom of the hill?

A) 185.22 J

B) 1,006.26 J

C) 3,145.50 J

D) 2,920.53 J

Answer 1

The correct answer is C) 3,145.50 J, which represents the amount of kinetic energy the child and sled have at the bottom of the hill, considering that all potential energy is converted into kinetic energy in the absence of friction.

Step-by-step explanation:

Calculating Kinetic Energy at the Bottom of the Hill

The question relates to the conversion of potential energy to kinetic energy as the child and sled slide down the hill. Since there is no friction, all the potential energy at the top of the hill is converted to kinetic energy at the bottom. The potential energy at the top of the hill can be calculated using the formula PE = m × g × h, where m is the mass, g is the acceleration due to gravity (approximately 9.81 m/s² on Earth), and h is the height of the hill. To find the kinetic energy (KE) at the bottom of the hill, we use the potential energy which should be equal to KE due to the conservation of energy principle. Hence, KE = m × g × h. Substituting the given values: KE = 54 kg × 9.81 m/s² × 6.9 m, we then get the kinetic energy.

KE = 54 kg × 9.81 m/s² × 6.9 m = 3,145.50 J

Therefore, the correct answer is C) 3,145.50 J. This is the amount of kinetic energy the child and sled will have at the bottom of the hill.