- 36

- 0

**1. Homework Statement**

A steamer starts from rest, the engine exerting a constant propelling force Mf, where M is the mass of the steamer. The resistance of the steamer is assumed to vary as the square of the speed. Show that the distance x travelled in time t is:

x = (V^2 /f) ln cosh (f*t/V ) where V is the full speed of the steamer.

**2. Homework Equations**

**3. The Attempt at a Solution**

I am not sure whether I understood what is happening in this system correctly but I got the following equation:

Mf - v

^{2}M = Ma

f - v

^{2}= a

Then, I tried solving it to find x(v) and I obtained:

x = 1/2 ln({f}/{f-V

^{2}})

I got a similar expression for v(t):

t = arcsin (V/√f)

But then I am not sure how one an obtain an expression with all three variables in it (i.e. x, V and t)

Thank you in advance!