Tarzan, who weighs 688 N, is preparing to swing from a cliff using a vine tied t

Question

Tarzan, who weighs 688 N, is preparing to swing from a cliff using a vine tied to the top of a palm tree. His friend Jane (who was always the better scientist) has estimated the length of the vine to be 18.0 ± 0.7m, and the distance from the top of the cliff to the lowest point of the swing (directly below the anchor point on the tree) to be 3.2 ± 0.2m. Her estimations are important, since they both know the vine will break if the force on it exceeds 950 N. Based on the information available, would you recommend that Tarzan swing from the cliff? Show all work needed to give your most quantifiable recommendation to help Tarzan make the most informed decision possible before stepping off that cliff.

(* Partial Derivatives Problem)

Explanation / Answer

length =L=18m

height tension in the string at lowest point ,which is equal to

T =mg +mv2/L----(1)

initial height of the Tarzan(anchor point ) =Y=3.2m

let final point is lowest point of string

by energy conservation

initial energyat initial point =final energy at final point

mgY =1/2 mv2

v2 =2gY ---(2)

from eq(1) and (2) we get....

T =mg +2mgY/L

given :- mg =688N and max T =950N

T =688 +2*688*3.2/18 =932.7 N

if L =18-0.7=17.3 and Y =3.2+0.2=3.4

then T =688+2*688*3.4/17.3 =958.4277 in this case vine is break .....

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

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