Jane, whose mass is 50kg, needs to swing across a river (having width d) filled

Question

Jane, whose mass is 50kg, needs to swing across a river (having width d) filled with man eating crocodiles to save Tarzan from danger. However, she must swing into a wind exerting with constant
horizontal force F on a vine having length L and initially making an angle ? with the vertical. Taking d=50m, F=110N, L=40m, and ?=50degrees.
a) With what minimum speed must Jane begin to swing to just make it to the other side?
b) Once the rescue is complete, Tarzan and Jane must swing back across the river. With what minimum speed must they begin their swing? Assume Tarzan has a mass of 80kg.
Answer: Part a) D = Lsin + Lsinf, 50=40(sin50+sinf), f = 28.9 degrees Ki + Ui + Wwind = Kf + Uf 1/2mvi2 + mg(-Lcos) + FD(-1)=0+mg(-Lcosf) 1/2(50)(vi)2 + 50(9.8)(-40cos50)-110(50) = 50(9.8)(-40cos28.9)
vi = 6.15 m/s Part b) 1/2mvi2 + mg(-Lcosf) + FD(+1) = 0+mg(-Lcos) 1/2(130)(vi)2 + 130(9.8)(-40cos28.9)+110(50) = 130(9.8)(-40cos50) vi = 9.87 m/s
I know the answer, but i just need to do it in A B C D method. step a, list the givens and unknowns. step b, write down formulas that you will use. step c, change up the formula to find the unknowns or the information that you need to figure out. step d, plug in the numbers or in other words the givens to solve the problem. I need both parts A and B to be in the A B C D method.
Jane, whose mass is 50kg, needs to swing across a river (having width d) filled with man eating crocodiles to save Tarzan from danger. However, she must swing into a wind exerting with constant
horizontal force F on a vine having length L and initially making an angle ? with the vertical. Taking d=50m, F=110N, L=40m, and ?=50degrees.
a) With what minimum speed must Jane begin to swing to just make it to the other side?
b) Once the rescue is complete, Tarzan and Jane must swing back across the river. With what minimum speed must they begin their swing? Assume Tarzan has a mass of 80kg.
Answer: Part a) D = Lsin + Lsinf, 50=40(sin50+sinf), f = 28.9 degrees Ki + Ui + Wwind = Kf + Uf 1/2mvi2 + mg(-Lcos) + FD(-1)=0+mg(-Lcosf) 1/2(50)(vi)2 + 50(9.8)(-40cos50)-110(50) = 50(9.8)(-40cos28.9)
vi = 6.15 m/s Part b) 1/2mvi2 + mg(-Lcosf) + FD(+1) = 0+mg(-Lcos) 1/2(130)(vi)2 + 130(9.8)(-40cos28.9)+110(50) = 130(9.8)(-40cos50) vi = 9.87 m/s
I know the answer, but i just need to do it in A B C D method. step a, list the givens and unknowns. step b, write down formulas that you will use. step c, change up the formula to find the unknowns or the information that you need to figure out. step d, plug in the numbers or in other words the givens to solve the problem. I need both parts A and B to be in the A B C D method.

Explanation / Answer

a)The mass of Jane is m = 50 kg The width of the river is d = 50 m The length of the vine is L = 40 m The angle made by the vine with the vertical is ? = 50 degrees = 50 * (p/180) radians = 0.872 radians The force is F = 110 N We know from the relation d = L * ?1 where ?1 is the angle made by the vine when Jane reaches the opposite side. or ?1 = (d/L) The angular displacement is ?? = ?1 - ? The time taken by Jane to cross the river is d = ut + (1/2)gt2 where u = 0 and g = 9.8 m/s2 or t2 = (2d/g) or t = (2d/g)1/2 The angular velocity is w = (??/t) We know that v = L * w or v = L * (??/t) ----------(1) where v is the minumum speed with which Jane must swing across the river. b)The mass of Tarzan is m = 80 kg From equation (1),we find that the minimum speed is independent of mass.Hence while returning the speed should be the same. The angular velocity is w = (??/t) We know that v = L * w or v = L * (??/t) ----------(1) where v is the minumum speed with which Jane must swing across the river. b)The mass of Tarzan is m = 80 kg From equation (1),we find that the minimum speed is independent of mass.Hence while returning the speed should be the same.

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