Question

In the winter sport of bobsledding, athletes push their sled along a horizontal ice surface and then hop on the sled as it starts to careen down the steeply sloped track. In one event, the sled reaches a top speed of 9.2 m/s before starting down the initial part of the track, which is sloped downward at an angle of 9.0 ∘.

What is the sled's speed after it has traveled the first 100 m ?

Answer 1

Answer: approximately 13.6 m/s.

Explanation: The sled's speed after it has traveled the first 100 m can be determined using the principles of kinematics. We can use the equations of motion to solve this problem.

First, let's identify the given information:

- Initial speed (v₀) = 9.2 m/s (sled's top speed before starting down the track)

- Distance traveled (s) = 100 m (the first 100 m of the track)

- Angle of the slope (θ) = 9.0° (angle of the track)

To find the sled's speed after traveling 100 m, we need to determine the final speed (v) using the equation of motion that relates initial speed, final speed, distance, and angle:

v² = v₀² + 2as

Here's how we can calculate it step by step:

Convert the angle from degrees to radians:

θ = 9.0° = (9.0° * π) / 180 ≈ 0.157 radians

Determine the acceleration (a) using the gravitational acceleration and the angle of the slope:

a = g * sin(θ)

g ≈ 9.8 m/s² (acceleration due to gravity)

a ≈ 9.8 m/s² * sin(0.157) ≈ 1.36 m/s²

Substitute the known values into the equation of motion:

v² = (9.2 m/s)² + 2 * (1.36 m/s²) * (100 m)

Simplify and solve for v:

v ≈ √(9.2² + 2 * 1.36 * 100) ≈ 13.6 m/s

Therefore, the sled's speed after traveling the first 100 m is approximately 13.6 m/s.