Question

A 65-kg ice skater is gliding along at 4.5 m/s. Twenty seconds later, her speed has dropped to 2.9 m/s. What is the magnitude of the kinetic friction acting on her skates?

Option 1: 25 N
Option 2: 35 N
Option 3: 45 N
Option 4: 55 N

Answer 1

Calculating the skater's deceleration and applying Newton's second law reveals that the kinetic friction force is 5.2 N, which doesn't match any of the provided options. There may be an error in the question's supplied values or options.

Step-by-step explanation:

To determine the magnitude of the kinetic friction acting on the ice skater, we first need to find the deceleration of the skater. This is calculated using the change in velocity divided by the time period over which the change occurs. Using the final velocity (v_f = 2.9 m/s) and the initial velocity (v_i = 4.5 m/s) with the time period of 20 seconds, the deceleration (a) is:

a = (v_f - v_i) / t

a = (2.9 m/s - 4.5 m/s) / 20 s

a = -1.6 m/s² / 20 s

a = -0.08 m/s²

The negative sign indicates that this is a deceleration. The force of kinetic friction can be calculated using Newton's second law, F = ma, where m is the mass of the skater and a is the deceleration:

F_friction = m * |a|

F_friction = 65 kg * 0.08 m/s²

F_friction = 5.2 N

However, none of the given options match this result, suggesting there may be a mistake in the provided options or in the provided data for the question.