Question

1. (5pts) we discussed projectile motion with a drag force which leads to a terminal velocity, ( v_t ). if the velocity ( v_t ) is given by ( v_t=\frac{mg}{b} ) where ( m ) is the objects mass, ( g ) is the acceleration due to gravity, and ( b ) is the drag coefficient. find the units of ( b ).

Explanation:

Step1: Analyze the units of each variable

• \(v_t\) (terminal velocity) has units of \(m/s\) (meters per second).
• \(m\) (mass) has units of \(kg\) (kilograms).
• \(g\) (acceleration due to gravity) has units of \(m/s^{2}\) (meters per second squared).

Step2: Rearrange the formula to solve for \(b\)

From \(v_t=\frac{mg}{b}\), we can rewrite it as \(b = \frac{mg}{v_t}\).

Step3: Substitute the units

Substitute the units of \(m\) (\(kg\)), \(g\) (\(m/s^{2}\)) and \(v_t\) (\(m/s\)) into the formula for \(b\).

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Answer:

The units of \(b\) are \(kg/s\) (kilograms per second).