A girl coasts down a hill on a sled, reaching

level ground at the bottom with a speed of
7.0 m/s. The coefficient of kinetic friction
between the sled’s runners and the hard, icy
snow is 0.054, and the girl and sled together
weigh 749 N.
The acceleration of gravity is 9.81 m/s
2
.
How far does the sled travel on the level
ground before coming to a rest?

To find the distance that the sled travels on the level ground before coming to a rest, we need to calculate the deceleration caused by the kinetic friction between the sled's runners and the snow.

First, let's calculate the force of kinetic friction using the formula:
Frictional force = coefficient of kinetic friction * normal force

The normal force is equal to the weight of the girl and sled, which is given as 749 N.

Frictional force = 0.054 * 749 N
Frictional force = 40.446 N

Next, let's calculate the deceleration caused by the kinetic friction using Newton's second law:
Frictional force = mass * acceleration

The mass of the girl and sled can be found using the weight and acceleration due to gravity:
Weight = mass * acceleration due to gravity

749 N = mass * 9.81 m/s^2

Solving for mass:
mass = 749 N / 9.81 m/s^2
mass ≈ 76.38 kg

Now we can substitute the values into the equation:
40.446 N = 76.38 kg * acceleration

Solving for acceleration:
acceleration = 40.446 N / 76.38 kg
acceleration ≈ 0.529 m/s^2

Finally, we can use the kinematic equation to find the distance traveled by the sled:
v^2 = u^2 + 2as

Where:
v = final velocity (0 m/s, as the sled comes to rest)
u = initial velocity (7.0 m/s)
a = acceleration (-0.529 m/s^2)
s = distance traveled (to be calculated)

Rearranging the equation:
s = (v^2 - u^2) / (2a)

Plug in the values:
s = (0^2 - 7.0^2) / (2 * (-0.529))
s ≈ 49.82 m

Therefore, the sled travels approximately 49.82 meters on the level ground before coming to a rest.