Question

A sled takes off from the top of a hill inclined at 6.0⁰ to the horizontal. The sled's initial speed is 12 m/s. The coefficient of kinetic friction between the sled and the snow is 0.14 . Determine how far the sled will slide before coming to a rest.

Answer 1

The sled will slide 30.11 meters before coming to a rest.

Step-by-step explanation:

The distance the sled slides can be calculated using the following formula:

d = v₀²/2a

where:

d is the distance the sled slides (meters)

v₀ is the initial speed of the sled (meters per second)

a is the acceleration of the sled (meters per second squared)

We can calculate the acceleration of the sled using the following formula:

a = g - μk g sinθ

where:

g is the acceleration due to gravity (9.81 meters per second squared)

μk is the coefficient of kinetic friction

θ is the angle of inclination of the hill (degrees)

Plugging in the given values, we get:

a = 9.81 m/s² - 0.14 ⋅ 9.81 m/s² ⋅ sin(6.0°) ≈ 7.19 m/s²

Plugging in the values for v₀ and a, we get:

d = (12 m/s)² / (2 ⋅ 7.19 m/s²) ≈ 30.11 m

Therefore, the sled will slide 30.11 meters before coming to a rest.