A skier slides horizontally along the snow for a distance of 20.8 m before coming to rest. The coefficient of kinetic friction between the skier and the snow is 0.0449. Initially, how fast was the skier going?
To find the initial speed of the skier, we can use the equation of motion, which relates the distance traveled, the initial speed, and the coefficient of kinetic friction.
The equation is:
distance = (initial speed^2) / (2 * coefficient of kinetic friction * gravitational acceleration)
In this case, the distance traveled is given as 20.8 m, and the coefficient of kinetic friction is 0.0449. The gravitational acceleration is approximately 9.8 m/s^2.
Using this information, we can rearrange the equation to solve for the initial speed:
initial speed^2 = (2 * coefficient of kinetic friction * gravitational acceleration * distance)
initial speed^2 = (2 * 0.0449 * 9.8 * 20.8)
initial speed^2 = 4.6724
Taking the square root of both sides, we get:
initial speed = √(4.6724)
initial speed ≈ 2.16 m/s
Therefore, the initial speed of the skier was approximately 2.16 m/s.