Final answer:
To determine the length of the slope, we use the given information and apply kinematics principles to calculate the acceleration along the slope. We can then use the kinematic equation to solve for the distance along the slope. The correct answer is 20 seconds.
Step-by-step explanation:
To determine the length of the slope, we need to use the given information and apply the principles of kinematics. The sled starts from rest, so its initial velocity is 0 m/s.
The slope is at an angle of 15°, which means we can decompose the acceleration due to gravity into two components: parallel to the slope and perpendicular to the slope. The parallel component of gravity accelerates the sled down the slope, while the perpendicular component doesn't affect the motion along the slope.
Using the given information that the trip to the bottom takes 10 s and the kinematic coefficient is 0.20, we can calculate the acceleration along the slope using the formula:
a = g * sin(θ) - k * g * cos(θ)
With θ = 15°, g = 9.8 m/s², and k = 0.20, we can substitute these values into the formula to find the acceleration. Once we have the acceleration, we can use the kinematic equation s = ut + 0.5at²
where s is the distance along the slope, u is the initial velocity, a is the acceleration, and t is the time.
By rearranging the equation, we can solve for s:
s = 0.5at²
Since the initial velocity is 0 m/s, u = 0, we can calculate the distance along the slope using the known values of the acceleration and time.
The correct answer is (c) 20 seconds.