Gayle runs at a speed of 9.00 m/s and dives on a sled, initially at rest on the top of a frictionless, snow-covered hill, that has a vertical drop of 20.0 m. After she has descended a vertical distance of 4.00 m, her brother, who is initially at rest, hops on her back, and they continue down the hill together. What is their speed at the bottom of the hill?

Question

Gayle runs at a speed of 9.00 m/s and dives on a sled, initially at rest on the top of a frictionless, snow-covered hill, that has a vertical drop of 20.0 m. After she has descended a vertical distance of 4.00 m, her brother, who is initially at rest, hops on her back, and they continue down the hill together. What is their speed at the bottom of the hill?

Gayle’s mass is 70.0 kg, the sled has a mass of 2.00 kg, and her brother has a mass of 50.0 kg.

Answer 1

energies gained=final energy

HerPE+HisPE+herinitalKE+hisInitialKE= finalcombinedKE + finalPE

+G*9.8*20+B*9.8*16 +1/2 G 9^2+ 0=1/2 (G+B)Vf^2+0

G is her mass, B is brothers mass, Vf is the finalspeed at bottom.
check my thinking.

Answer 2

I don't think I am getting the right value, what are you getting?

Answer 3

To find the speed of Gayle and her brother at the bottom of the hill, we can use the principle of conservation of mechanical energy.

First, let's calculate the potential energy at the top of the hill (before Gayle starts sliding):

Potential Energy = mass * gravitational acceleration * height
= (70.0 kg + 2.0 kg + 50.0 kg) * 9.8 m/s^2 * 20.0 m
= 122.0 kg * 9.8 m/s^2 * 20.0 m
= 23920 J

Next, let's calculate the potential energy after Gayle has descended a vertical distance of 4.00 m:

Potential Energy = (70.0 kg + 2.0 kg + 50.0 kg) * 9.8 m/s^2 * 4.00 m
= 122.0 kg * 9.8 m/s^2 * 4.00 m
= 4772.8 J

The difference in potential energy between the top and the point where her brother hops on is given by:

Potential Energy Difference = Potential Energy at top - Potential Energy at 4.00 m
= 23920 J - 4772.8 J
= 19147.2 J

This energy difference is converted into the kinetic energy of Gayle, the sled, and her brother at the bottom of the hill.

Kinetic Energy = (1/2) * (Total mass) * (Speed)^2

We can now solve for the speed (V) using the formula:

Kinetic Energy = 19147.2 J
Total mass = 70.0 kg + 2.0 kg + 50.0 kg = 122.0 kg

19147.2 J = (1/2) * 122.0 kg * V^2

We can rearrange the equation to find the value of V:

V^2 = (2 * 19147.2 J) / 122.0 kg

V^2 = 315.501639 meters squared per second squared

V = sqrt(315.501639)

V ≈ 17.74 m/s

Therefore, the speed of Gayle and her brother at the bottom of the hill is approximately 17.74 m/s.