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## Homework Statement

A point mass m falls from rest through a height h. The frictional force is given by [tex]-\gamma \dot{z}[/tex] and gravity by [tex]-mg[/tex].

Give the 'equation of motion' (differential equation) for the height z(t).

## The Attempt at a Solution

[tex] \ddot{z} = -g - \frac{\gamma}{m} \dot{z}[/tex]

I thought about integrating then rearranging:

[tex]\Rightarrow \dot{z} = -gt - \frac{\gamma}{m}z +c_{1}[/tex]

[tex]\Rightarrow z(t) = - \frac{m}{\gamma} (\dot{z} + gt + c_{1})[/tex]

The question the asks what kind of differentional eq. this is and asks the student to make the following substitution:

[tex]\dot{z}(t) = v(t)[/tex]

and asks what kind of equation it is now! Well I haven't got a clue what its is on about. I assume something like [tex]s = ut +\frac{1}{2}at^{2}[/tex] should come out. Have to hand this in tomorrow so please help!