Conservation of Energy w/ Tarzan & Jane

[njvc3]

Hello, I was looking for some help. please...

I've been struggling with the following problem:

Jane, whose mass is 50kg, needs to swing across a river filled with crocs in order rescue Tarzan, whose mass is 80kg. However, she must swing into a constant horizontal wind Force (110 N) on a vine (L=40m) that is initially at an angle of (theta=50) with the vertical. and the distance of the river she must cross is D=50 m. (The diagram displays the height Jane is at inititally to be a little higher than the height of the bank Tarzan is at)
a) What is the minimum speed Jane must begin her swing in order to just make it to the other side?
b) Once the rescue is complete, Tarzan and Jane must swing back together across the river. What is the minimum speed they must begin their swing?


I tried to figure out the height by figuring out how much Potential Energy she has.. Change in net Energy is 0; so using the Conservation of Energy equation: delta KE + delta Epot + deltaEwind = 0

figuring the final velocity (that she lands at) is 0 and the change in final height is 0... I'm left with the following equation:
(1/2m*(initial v)^2)+(m*g*delta h initial)-(Force wind*D)

where the only information I don't have is the initial v and delta h initial.


The answers are supposed to be a)6.15m/s & b) 9.87m/s ... but, i can't seem to get it..

Thanks.

 

[Dr.Brain]

a) Apply conservationa of energy . Use the angles given to calculate the height difference.

BJ

 

[Päällikkö]

This is my first time posting on the forums and I'm not a native English speaker, plus I'm unfamiliar with the proper Physics terms, so bear with me.


Jane starts at 50 degrees, and lands at \alpha = arcsin(D/L - cos40) = 28,94406598 degrees (compared to the vertical line), which you can get by applying basic trigonometry. Now you should be able to solve the difference in height.

W = FL[sin50 + sin \alpha] = 5500 J (I went through some integrating but, of course, got the same answer as you'd get with W = FD)

 

[pete worthington]

Hello, I was looking for some help. please...

I've been struggling with the following problem:

... (The diagram displays the height Jane is at inititally to be a little higher than the height of the bank Tarzan is at)...

There appears to be some missing information. Is this height difference labeled? Is the vine placed between the river (25 m from each side)? I just love these tarzan and Jane swinging problems. This one appears to be straight forward but the drawing or more clarification would be helpful.

 

[OlderDan]

There appears to be some missing information. Is this height difference labeled? Is the vine placed between the river (25 m from each side)? I just love these tarzan and Jane swinging problems. This one appears to be straight forward but the drawing or more clarification would be helpful.

There is enough information given. The position of the vine relative to the river is determined by its length and the initial angle.

 

[Maxos]

You shoud use the theorem of kinetic energy:

W=K2-K1=-K1 (K2 is at least 0)
W=W(gr)+W(wind)
=-(U2-U1)-integral(from theta1 to -theta2 which you determine with geometric reasons)[M*dtheta]

U is the potential energy for gravity.
M=F*r*sin(theta+pi/2); integral[M*dtheta]=-F*r*(sin(theta1)+sin(theta2))

They are all simple calculations.

 

[njvc3]

Thank you all..

Thanks for your insight.. That is exactly what I was not understanding.. I did have to use the angle. Thanks!