A boat with initial speed v is launched on a lake. The boat is slowed by the water by a force, F=-ke^(bv). Find the expression for speed v(t).(adsbygoogle = window.adsbygoogle || []).push({});

I've done the problem, but my answer seems too odd to be right...it may be my calculus.

I've drawn a FBD, with the normal force and weight cancelling each other out. The net force is the resisting force, F=-ke^(bv), which I've then set equal to F=ma. I've used dv/dt for a.

-ke^(bv)=m*(dv/dt)

Rearranging to get like terms together gives me

dv/(e^(bv))=-(k/m)dt

(e^-(bv))dv=-(k/m)dt

Setting up the integrand using limits 0 to t and initial v to v gives me:

-b((e^-(bv.initial))-(e^-(bv)))=-(k/m)t

Simplified to:

(kt/bm)=e^(v.initial/v)

ln (kt/bm)=(v.inital/v)

So, v=(v.initial)/ln(kt/bm)

The answer seems too messy...any help would be much appreciated!

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# Homework Help: Newtonian Mechanics

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