# Velocity

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All work must be shown step by step, any answers given without proper justification will not be accepted. Keep track of units and use proper notation.

An object is dropped from a tall building, If the air resistance is proportional to the square of the velocity, then (dv/dt)=-32(ft/sec^2)+kv^2 where k is a constant. Show that the velocity v as a function of time is v(t)= [squareroot(32/k)][tanh(squareroot(32kt))]

https://brainmass.com/physics/velocity/proportional-velocity-word-problem-22254

#### Solution Preview

Please see the attachment.

, we need to find .

First, let's clarify some definitions.

, , .

So ...

#### Solution Summary

This shows how to work with velocity and time.

$2.49