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 downward when it is falling downward at .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

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  downward when it is falling downward at  .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

Quizplus · Accepted Answer

We can use the equation for the net force on the object:

F_net = m*a = m*g - kv^2

where m is the mass of the object, g is the acceleration due to gravity (9.81 m/s^2), k is the constant of proportionality for the drag force, and v is the speed of the object.

At terminal speed, the acceleration is zero, so we have:

0 = m*g - kv_terminal^2

Solving for v_terminal, we get:

v_terminal = sqrt(m*g/k)

Substituting in the given values, we get:

v_terminal = sqrt((30.0 kg)*(9.81 m/s^2)/((30.0 kg/s^2)*(11.0 m/s)))

v_terminal = 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