A seaplane of mass of mass m flying at a speed Vo lands on a lake and glides to

Question

A seaplane of mass of mass m flying at a speed Vo lands on a lake and glides to a rest along a straight line path. Because the planes engines are turned off at the point of landing, the only horizontal force on it at it glides is the resistive force exerted by the water. At any instant during gliding, the resistive force Fr is proportional to the velocity v of the seaplane, i.e. Fr=-bv where b is the drag coeffiicient. The speed Vt of the seaplane at time t after touching down on water is ( assumption that its done using calculus and intregals. not sure what to do. Thanks for any help. This is a rush response request if possible.

Explanation / Answer

Fr=-bv

mdv/dt=-bv

mdv/v=-bdt

mlnv=-bt+c

mlnv=-bt+mlnv0

v=e^-(bt/m+lnv0) exp for vt

where v0 is velocity at t=0

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