A 30.0-kg object experiences a drag force due to air resistance with a magnitude proportional to the square of its speed.The object falls with an acceleration of 4.00 m/s² downward when it is falling downward at 70.0 m/s.What is its terminal speed? A)110 m/s B)157 m/s C)91.0 m/s D)172 m/s E)108 m/s

Question

Quizplus · Accepted Answer

When the object reaches its terminal speed, the drag force is equal in magnitude to its weight, resulting in a net force of 0 and a constant velocity. At terminal speed, the drag force is given by:

F_drag = k v^2

where k is a constant and v is the velocity of the object.

At terminal speed, we have:

mg = k v_term^2

Solving for v_term, we get:

v_term = sqrt(g/k) * sqrt(m)

Substituting the given values, we get:

v_term = sqrt(4.00 m/s^2 / (k / 30.0 kg)) * sqrt(30.0 kg) = 91.0 m/s

Therefore, the answer is (C) 91.0 m/s.

A 300-Kg Object Experiences a Drag Force Due to Air Resistance