Jane, whose mass is 46.0 kg, needs to swing across a river (having width D ) fil

Question

Jane, whose mass is 46.0 kg, needs to swing across a river (having width D) filled with person-eating crocodiles to save Tarzan from danger. She must swing into a wind exerting constant horizontal force

Jane, whose mass is 46.0 kg, needs to swing across a river (having width D) filled with person-eating crocodiles to save Tarzan from danger. She must swing into a wind exerting constant horizontal force F arrow ,on a vine having length L and initially making an angle ? with the vertical (see below figure). Take D = 51.0 m, F arrow = 110 N, L = 40.0 m, and = 45.0 degree. (b) Once the rescue is complete, Tarzan and Jane must swing back together across the river. With what minimum speed must they begin their swing? Assume that Tarzan has a mass of 84.8 kg.

Explanation / Answer

mj=46.0kg, mt=84.8kg, D=51.0m, L=40.0m, Fw=110N, =45o, =?, vo=?

First break up D in order to find . Notice that L and a portion of D make up a triangle.

D2 will be the second part of D: D2=Lsin() or 40(sin(45)) or 20[2] Jane's vertical displacement can also be calculated using the pythagorean theorem. [(40)2-(20[2])2]=28.28427125; 40-28.28427125=11.71572875m

This is her displacement for the first part of the trip.

Now lets find D1 so we can find : D1=51.0-20[2]=22.71572875m. Now we have 2 sides of 's triangle the opposite and hypotenuse so lets find using inverse sin of the opposite over the hypotenuse.

sin-1((51.0-20[2])/(40))=; =34.60344377o Now to find +=79.60344377o

Now lets find Jane's diplacement for the second part of the trip now that is known using the pythagorean theorem. [(40)2-(51.0-20[2])2]= 32.9240894; 40-32.9240894=7.075910533m

So the total displacement is 11.71572875m-7.075910533m= 4.639818217m this is the heigh we will use for the gravitational potential energy

Now that all quantities have been found lets use the Work energy theorem to find their intial speed

Eo=(1/2)(mj+mt)(vo2), Wnc=Fw(sin(+))(d), Ef=(m)(g)(h): Eo+|Wnc|=Ef

(1/2)(mj+mt)(vo2)+Fw(sin(+))(d)=(mt+mj)(g)(h) :solve for vo:

(1/2)(mj+mt)(vo2)=(mt+mj)(g)(h)-Fw(sin(+))(d)

(vo2)=((2)/(mj+mt))[(mt+mj)(g)(h)-Fw(sin(+))(d)]

vo=[((2)/(mj+mt))[(mt+mj)(g)(h)-Fw(sin(+))(d)]]

vo=[((2)/(130.8))[(130.8)(9.8)(4.639818217)-(110)(sin(79.60344377))(51)]]

vo=2.562991648(m/s) or 2.56(m/s)

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