Question

gravity and air resistance quick check
which is the equation for terminal velocity? (1 point)
$v_{t}=\sqrt{\frac{2m}{dac_{d}}}$
$v_{t}=\sqrt{\frac{2w}{dac_{d}}}$
$v_{t}=\sqrt{\frac{w}{2dac_{d}}}$
$v_{t}=\sqrt{\frac{dac_{d}}{2w}}$

Explanation:

Step1: Recall the formula for terminal velocity

Terminal velocity \(V_t\) occurs when the drag force \(F_d=\frac{1}{2}dAC_dV_t^2\) (where \(d\) is the air density, \(A\) is the cross - sectional area, \(C_d\) is the drag coefficient) is equal to the weight \(w\) of the object.

Set \(F_d = w\), so \(\frac{1}{2}dAC_dV_t^2=w\).

Step2: Solve for \(V_t\)

First, multiply both sides of the equation \(\frac{1}{2}dAC_dV_t^2 = w\) by \(2\) to get \(dAC_dV_t^2=2w\).

Then, divide both sides by \(dAC_d\): \(V_t^2=\frac{2w}{dAC_d}\).

Take the square root of both sides: \(V_t=\sqrt{\frac{2w}{dAC_d}}\).

Answer:

\(V_t=\sqrt{\frac{2w}{dAC_d}}\) (the second option)