Conservation of energy -swinging vine.

[frasifrasi]

Conservation of energy --swinging vine.

I am not sure how to do this question. I tried doing it but the answer differs from the book.

Here it is:

"A 17m long vine hangs vertically from a tree on one side of a 10 m wide hole. A person runs up, hoping to grab the vine, swing over the hole, and drop vertically off the vine to land on the other side. At what minimum speed must he be running?"

So, since this is in the conservation of energy,
you have

K2 + U2 = K1 + U1

I really have no clue how I can use this to solve the problem. Can anyone tell me how to get started, which equation I should use?

Thanks.

 

[Doc Al]

Figure out how high he'll be (and thus how much PE he'll need) when he just swings to the other side of the hole. You'll need to use a bit of trig/geometry. (Draw a careful diagram.)

 

[frasifrasi]

Thanks, I am having a little trouble getting the height. The tringle will be isosceles with two 17 m sides, but how do I find the base of the triangle? After I find this, I can calculate the y for the smaller triangle underneath with base 10 to give the height, correct?

 

[Doc Al]

The way I look at it, an easier triangle to analyze is a right triangle with hypotenuse equal to 17 m. (The hypotenuse is the vine at its highest angle.) The base of this triangle is 10 m.

 

[frasifrasi]

but why would it be 10 m if the vine doesn't touch the bottom of the hole at the end?

 

[frasifrasi]

Ok, so the difference between the vine and this height, will be how high he will need to be at the end, correct?

So, is the following set up correct?

1/2 mv^2 + 0 = mg(h = 3) + 0

He won't have any kinetic energy at the end, correct?

 

[Doc Al]

but why would it be 10 m if the vine doesn't touch the bottom of the hole at the end?

Because we want him just on the far side of the hole, 10 m away.

Ok, so the difference between the vine and this height, will be how high he will need to be at the end, correct?

The difference between the length of the vine and the height of the triangle will be how high the person will be at the end (compared to where he started).

So, is the following set up correct?

1/2 mv^2 + 0 = mg(h = 3) + 0

Where did you get h = 3? (Be more precise.)

He won't have any kinetic energy at the end, correct?

Right.

 

[frasifrasi]

Well, the height of the triangle we used was ~14, so 17-14 = 3.

Just confirming, thanks.