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I don't know if I do it right, if someone please verify me, Thank You.

Given a boat with mass 'm' and travelling with speed V

_{m}.

There are two forces acting on the boat. The force of water resistance which is

dependent on boat's speed relatively to the water and given by

[tex]\vec{f}[/tex]=-bv

^{2}

and the force of the engine. Assume that the motion is linear and the water

is stationary. In order to stop the boat the engine rotation direction is reversed.

a)Find the motion equation

b)Find the engine force

c)Find the boat's speed as a function of time

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a)

fw-water resistance force

f - engine force

[tex]\Sigma[/tex]F=ma

V

^{2}=V

_{0}

^{2}- 2*a*X

V

_{0}=V

_{m}

V=0

=>V

_{m}

^{2}=2*a*X =>

X=V

_{m}

^{2}/2*a => X=V

_{m}

^{2}/m*2*(fw+f)

b)

V=V

_{0}-a*t => V

_{m}=a*t =>

V

_{m}=(f+fw)*t/m

f = Vm*m/t-fw

c)

V=V

_{0}+a*t=V

_{m}-(f+fw)*t/m