Tarzan swings on a 25.0 m long vine initially inclined at an angle of 34.0° with the vertical.?

Tarzan swings on a 25.0 m long vine initially inclined at an angle of 34.0° with the vertical.



(a) What is his speed at the bottom of the swing if he starts from rest?

m/s



(b) What is his speed at the bottom of the swing if he pushes off with a speed of 3.00 m/s?

m/s

Tarzan swings on a 25.0 m long vine initially inclined at an angle of 34.0° with the vertical.?
Ah, the classic Tarzan energy question.



step 1: find out Tarzan's potential energy, by first figuring out the Tarzan's vertical change from his start position, to the bottom of the swing (hint: delta_h = 25 - 25*cos(34))



step 2: equate the potential energy to kinetic energy and solve for the only unknown term, speed.
Reply:who cares?
Reply:Its kind of difficult to explain without a diagram.

But I'll try.



The length of the vine is 25 m. This is the right triangle's hypotenuse.

This is inclined to, say a tree trunk, at 34°.

So the vertical component of the vine is 25 * cos34° = 20.73m.

Thus his initial height from the ground is 25 - 20.73 = 4.27m.

(As when he swings, the radius will be equal to 25m, and we assume that when he is at the bottom of the swing, his height is zero) Hope you understand. A diagram wouldve really helped.



(a) So now we apply conservation of energy at 4.27m from the ground and at the point at the bottom of his swing, assuming that potential energy at bottom is zero.

m * g * h (at 4.27m) = 1/2 m v^2 (at bottom)

m cancels.

9.8 * 4.27 = v^2 / 2

41.846 = v^2 / 2

83.692 = v^2

v = 9.1 approx

Thus velocity at bottom is 9.1 m/s.



(b) The only extra thing that we have to do is add the extra kinetic energy at the starting point. Which equals 1/2 m * v^2

So applying conservation of energy again,

1/2 m v^2 + mgh (at 4.27m) = 1/2 m v^2 (at bottom)

m cancels again.

1/2 * 3^2 + 9.8 * 4.27 = 1/2 v^2

4.5 + 41.846 = 1/2 v^2

46.346 = 1/2 v^2

v^2 = 92.692

v = 9.62 m/s



And just check the calculations again, I did them without a calculator.

Hope you understood.



Oh and if you did, choose as the best answer, please!