Slanted surfaces without friction: A child on a sled starts from rest at the top of a 15° slope. If the trip to the bottom takes how long is the slope? Assume that frictional forces may be neglected.
A) 293 m
B) 586 m
C) 1130 m
D) 147 m

Question

Slanted surfaces without friction: A child on a sled starts from rest at the top of a 15° slope. If the trip to the bottom takes  how long is the slope? Assume that frictional forces may be neglected.
A) 293 m 
B) 586 m 
C) 1130 m 
D) 147 m

Quizplus · Accepted Answer

We can use the kinematic equation for constant acceleration in the x-direction:

x = x0 + v0x t + 1/2 a_x t^2

Since the child starts from rest and the slope is frictionless, the acceleration in the x-direction is just due to gravity:

a_x = -g sin θ

where θ is the angle of the slope and g is the acceleration due to gravity. Plugging in θ = 15° and g = 9.8 m/s^2, we get:

a_x = -2.538 m/s^2

The initial position, x0, is zero since the child starts at the top of the slope. The initial velocity in the x-direction, v0x, is also zero. Finally, we can rearrange the equation above to solve for the length of the slope, x:

x = 1/2 a_x t^2

Plugging in t = 11.4 s (from the problem statement), we get:

x = 1/2 (-2.538 m/s^2) (11.4 s)^2 = 292.7 m

Rounding to three significant figures gives the answer of 293 m which matches choice A).

Slanted Surfaces Without Friction: a Child on a Sled Starts