Starting from rest, a 30.8 kg child rides a 9.75 kg sled down a frictionless ski slope. At the bottom of the hill, her speed is 6.0 m/s. If the slope makes an angle of 15.1 ° with respect to the horizontal, how far along the hill did she slide on her sled?

s = 7.044 m

Explanation:

Given:

- The mass of child Mc = 30.8 kg

- The mass of sledge Ms = 9.75 kg

- The slope θ = 15.1°

- The speed of of sledge at bottom vf = 6.0 m/s

- The initial velocity at top vi = 0

Find:

- We will apply the conservation of energy principle on the system consisting of child and sledge. The change in potential energy ΔP. E of the system from top to bottom gives rise to change in kinetic energy ΔK. E.

ΔP. E = ΔK. E

(Mc + Ms) * g*h = 0.5 * (Mc + Ms) * (vf^2 - vi^2)

Where, h: the change in vertical height

h = 0.5 * (vf^2 - vi^2) / g

h = 0.5*vf^2 / g

h = 0.5*6.0^2 / 9.81

h = 1.835 m

- The distance traveled along the slope (s) can be calculated by trigonometric ratio:

sin (θ) = h / s

s = h / sin (θ)

s = 1.835 / sin (15.1)

s = 7.044 m