Question

You are snowboarding down a hill at 13 m/s when you start sliding across a frozen lake. The frictional force slowing you down is 22 N. If your mass is 75 kg, how far do you slide?

Answer 1

To find the distance you slide, you can use the equation d = (vf^2 - vi^2) / (2a), where vf is the final velocity, vi is the initial velocity, and a is the acceleration. Substitute the given values and calculate the distance to find that you will slide approximately 115.369 meters on the frozen lake.

Step-by-step explanation:

To find the distance you slide, you can use the equation:

d = (vf2 - vi2) / (2a)

where d is the distance, vf is the final velocity (0 m/s in this case), vi is the initial velocity (13 m/s in this case), and a is the acceleration.

Since the frictional force is the only force slowing you down, it is equal to the force of kinetic friction, which is given as 22 N. The equation for friction is:

f = μN

where f is the force of friction, μ is the coefficient of friction, and N is the normal force (equal to your weight).

To find the acceleration, we can rearrange the equation for friction:

a = (μN) / m

Substituting the given values, we have:

a = (22 N) / (75 kg) = 0.293 m/s2

Now we can substitute the values into the distance equation:

d = (0 m/s - 13 m/s)2 / (2 × 0.293 m/s2) = 115.369 m

So, you will slide approximately 115.369 meters on the frozen lake.