Solve.
-A 57-kg skateboarder on a 2-kg board starts coasting on level ground at 5 m/sec. Let k = 3.2 kg/sec. How long will it take the skater's speed to drop to 3 m/sec?
A) -9.42 sec
B) 9.10 sec
C) 0.32 sec
D) 9.42 sec

Question

Quizplus · Accepted Answer

The problem can be solved using the formula derived from Newton's second law and the concept of drag force, which is proportional to velocity (F = kv). The equation for the velocity v as a function of time t, given the initial velocity v0, mass m, and drag coefficient k, is v = v0 * e^(-kt/m). Rearranging to solve for t when v = 3 m/s, v0 = 5 m/s, m = 59 kg (57 kg for the skateboarder plus 2 kg for the board), and k = 3.2 kg/s, we get t = -(m/k) * ln(v/v0). Plugging in the values, we find t = 9.42 sec.

Solve. -A 57-Kg Skateboarder on a 2-Kg Board Starts Coasting on on Level