A professional skier reaches a speed of 55 m/s on a 30° ski slope.Ignoring friction,what was the minimum distance along the slope the skier would have had to travel,starting from rest?

A) 154.34 m
B) 178.22 m
C) 308.67 m
D) 5.61 m
E) 0.003 m

Question

A professional skier reaches a speed of 55 m/s on a 30° ski slope.Ignoring friction,what was the minimum distance along the slope the skier would have had to travel,starting from rest?
​
A) 154.34 m
B) 178.22 m
C) 308.67 m
D) 5.61 m
E) ​0.003 m

Quizplus · Accepted Answer

We can use the conservation of energy principle to solve this problem. The initial potential energy of the skier is given by mgh, where m is the mass of the skier, g is the acceleration due to gravity and h is the vertical height of the slope. The final kinetic energy of the skier is given by (1/2)mv^2, where v is the speed of the skier at the bottom of the slope. 
Equating the two energies, we get:
mgh = (1/2)mv^2
Canceling out the mass m, we get:
gh = (1/2)v^2
Substituting the given values, we get:
(9.8 m/s^2)(h) = (1/2)(55 m/s)^2
Solving for h, we get:
h = (1/2)(55^2)/(9.8)
h = 154.34 m
This is the vertical height of the slope. To find the minimum distance along the slope, we need to find the horizontal distance traveled. We can use trigonometry to do this. The horizontal distance is given by:
distance = vertical height / sin(theta)
where theta is the angle of inclination of the slope (30 degrees). Substituting the values, we get:
distance = 154.34 / sin(30)
distance = 308.67 m
Therefore, the minimum distance along the slope that the skier would have had to travel, starting from rest, ignoring friction, is 308.67 m. So, the correct answer is option C.

A Professional Skier Reaches a Speed of 55 M/s on a 30°