Jane, whose mass is 46.5 kg, needs to swing across a river (having width D) fill

Question

Jane, whose mass is 46.5 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, on a vine having length L and initially making an angle with the vertical (see below figure). Take D = 51.0 m, F = 100 N, L = 40.0 m, and = 45.0°. (a) With what minimum speed must Jane begin her swing to just make it to the other side? (If Jane can make it across with zero initial velocity, enter 0.) (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

Given: D=51.0 ; F=100N; L=40m Theta=45; Jane mass= 46.5 Kg ; Tarzan mass = 84.8 Kg

using conservation of energy we solve this question:

K + U(g) + U(w) = K + U(g) + U(w)
½ mv² + mgh + 0 = 0 + mgh + F(w)×D

½ mv² = mgh- mgh+ F(w)×D
½ v² = gh- gh+ F(w)×D/m
v² = 2(gh + F(w)×D/m)

h = - (h- h)
= h- h
= L cos - L cos
= L (cos - cos ) <<solve: = arcsin(D/L -sin ) >>
h= L (cos - cos(arcsin(D/L -sin )) <<plug into equation for velocity>>

v² = 2(gh + F(w)×D/m)

Solve the equation and you will get the minimum speed
--------------------------------

b) Tarzan and Jane when swing back across the river.

K + U(g) + U(w) = K + U(g) + U(w)
½ mv² + mgh+ F(w)×D = 0 + mgh + 0

½ mv² = mgh- mgh- F(w)×D
½ v² = gh- gh- F(w)×D/m
v² = 2(gh - F(w)×D/m) << h= - h>>

Put the values and just solve the equation.

Related Questions

Navigate

• Browse (All)
• Browse J
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.