Question

You are snowboarding down a hill at 21 m/s when you start sliding across a frozen lake. The frictional force slowing you down is 22 N. If your mass is 70 kg, how far do you slide?

Answer 1

To determine the distance a snowboarder slides to a stop on a frozen lake, calculate the deceleration using the frictional force and mass, then apply a kinematic equation with initial velocity, final velocity, acceleration, and distance.

Step-by-step explanation:

The scenario describes a snowboarder with a mass of 70 kg, moving at an initial velocity of 21 m/s across a frozen lake and coming to a stop due to a constant frictional force of 22 N. To find the distance the snowboarder slides, we must first calculate the deceleration using Newton's second law of motion. The frictional force acts opposite to the direction of motion, so we can write the equation F = ma, where F is the frictional force (22 N), m is the mass (70 kg), and a is the acceleration (which will be negative due to deceleration).

We solve for the deceleration, a, by rearranging the equation: a = F/m. Next, we use the kinematic equation that relates initial velocity (vi), final velocity (vf, which is 0 since the snowboarder comes to a stop), acceleration (a), and distance (d): vf2 = vi2 + 2ad. From this, we can solve for the distance the snowboarder slides.