Question

a frictionless roller coaster is given an initial speed of vi=10.00m/s , at the initial height h=100:00m,has a mass m=1000.0kg

Answer 1

Answer: Using conservation of energy, we can find the final speed of the roller coaster at the bottom of the hill:

Initial energy (at the top) = Potential energy + Kinetic energy

1/2 * m * vi^2 + m * g * h = 1/2 * m * vf^2 + m * g * 0

where m = 1000.0 kg is the mass of the roller coaster, vi = 10.00 m/s is the initial speed, h = 100.00 m is the initial height, g = 9.81 m/s^2 is the acceleration due to gravity, and vf is the final speed at the bottom of the hill.

Simplifying and solving for vf:

vf = sqrt(2 * g * h + vi^2)

Substituting the given values:

vf = sqrt(2 * 9.81 m/s^2 * 100.00 m + (10.00 m/s)^2)

vf = sqrt(1962.2)

vf ≈ 44.3 m/s

Therefore, the final speed of the roller coaster at the bottom of the hill is approximately 44.3 m/s.