What minimum speed must he be running?

AI Thread Summary
To determine the minimum speed Tarzan must run to swing across a 10m gorge using a 17m vine, the problem involves conservation of energy principles. The potential energy at the highest point of the swing can be equated to the initial kinetic energy, allowing the calculation of velocity without needing Tarzan's mass. The relevant equations include potential energy (U = mgh) and kinetic energy (KE = 1/2 mv^2), leading to the simplified relationship v = sqrt(2gh). The challenge lies in accurately calculating the height (h) above the gorge at the end of the swing, which can be approached using geometric relationships. Clarification of the figure or additional details may be necessary for a complete solution.
dflutedevil
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A 17m--long vine hangs vertically from a tree on one side of a 10m--wide gorge, as shown in the figure. Tarzan runs up, hoping to grab the vine, swing over the gorge, and drop vertically off the vine to land on the other side. What minimum speed must he be running?
 
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What have you tried so far? You must show some work.
 
I just need some direction that's all..I'm not really good at this...I don't need the whole answer...just maybe some direction
 
Hi I'm new here, currently enrolled in Physics 101 (algebra based, but I'm in calc 3 right now) and I'm also curious as to how to start this problem. Thank you.
 
This is a conservation of energy problem. Figure out how high Tarzan is from the base of the gorge at the end of his swing to give you your potential energy, from which you can calculate the initial kinetic energy, and thus his velocity.
 
well i got how high he was when he landed but how does that relate to potential energy. isn't that U=mgy. i don't have his mass? is there something I'm missing?
 
You don't need the mass if you assume that all of the kinetic energy he had in the beginning is transferred into potential energy at the end of the swing.
 
I'm confused...I'm sorry. I guess I don't understand the concepts...so the h that i got = the potential and kinetic energy? but still the kinetic energy equation equals 1/2mv^2 which still requires mass?
 
But if KE_i=PE_f and you expand out what kinetic energy and potential energy equal, do you need the mass?
 
  • #10
so is this right then...
1/2v^2=h thus...
v=sqrt(2h)
 
  • #11
Where did the g go?
 
  • #12
uhm... don't know...so
v=sqrt(2gh)
 
  • #13
Looks better, now the hard part is finding the height above the ground at the end of the swing.
 
  • #14
see i just used the triangle to find the hypotenuse and then subtracted 17 from that. is that how i was supposed to do it? or am i way off?
 
  • #15
Is there some way you could either scan and upload the figure or possible explain the figure in words? I don't have enough information and I'm genuinely interested in the problem and solution.
 

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