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

a high pressure system is a dense air mass that is usually cooler and drier than the surrounding air. a low pressure system is a less dense air mass that is usually wetter and warmer than the surrounding air.

in general, areas that experience high atmospheric pressure also experience fair weather. low pressure systems can cause the formation of clouds and storms. air usually flows from areas of high pressure to areas of low pressure..