Remarks Substituting the symbolic expression s v_B = squareroot 2 gh into the eq
ID: 1527215 • Letter: R
Question
Remarks Substituting the symbolic expression s v_B = squareroot 2 gh into the equation for the distance d shows that d is linearly proportional to h: Doubling the height doubles the distance traveled. Question Give two reasons why skiers typically assume a crouching position when going down a slope. (Select all that apply.) Air resistance is lower in the crouched position. Crouching decreases the mass of the skier. The ski poles push more effectively when they are more nearly horizontal. Crouching decreases the skier's inertia. The acceleration of gravity g is increased by crouching. Use the worked example above to help you solve this problem, a skier starts from rest at the top of a frictionless incline of height 20.0 m, as shown in the figure. As the bottom of the incline, the skier encounters a horizontal surface where the coefficient of kinetic friction between skis and snow is 0.187. Find the skier's speed at the bottom. How far does the skier travel on the horizontal surface before coming to rest? Use the values from PRACTICE IT to help you work this exercise. Find the horizontal distance the skier travels before coming to rest if the incline also has a coefficient of kinetic friction equal to 0.187. (The incline makes an angle theta = 20.0degree with the horizontal.)Explanation / Answer
Air resistance is lower in the crouched position.
The ski poles push more effectively when they are more near horizontal.
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(a)
Velocity at bottom = (2*g*h)0.5 = (2*9.8*20)0.5 = 19.80 m/s
(b)
Assuming mass of skier as 'm' kg
Friction force, f = 0.187*m*9.8 = 1.83*m Newtons
Using energy balance:
Energy at bottom = Work done against friction to come to rest
0.5 * m * 19.82 = 1.83*m * x
Thus, x = 107.11 m
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This time, the energy balance equation is:
0.5*m*19.82 = 1.83*m*( 20 / tan(200) ) + 1.83*m*x
So, x = 52.17 m