Gravitational potential energy of tarzan

In summary, Tarzan uses a vine with a length of 20 m and angles of 45 degrees and 30 degrees to swing from one tree to another where Jane is waiting. Ignoring air resistance and the mass of the vine, the problem asks to calculate Tarzan's speed just before he reaches Jane. The solution involves using the equation K_1 + U_1= K_2 + U_2, where K represents kinetic energy and U represents potential energy. The given angle measurements are used to determine the change in height and calculate the kinetic energy.
  • #1
djgomez
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Homework Statement



Tarzan, in one tree, sights Jane in another tree. He grabs the end of a vine with length 20 m that makes an angle of 45 degrees with the vertical, steps off his tree limb, and swings down and then up to Jane's open arms. When he arrives, his vine makes an angle of 30 degrees with the vertical.

Calculate Tarzan's speed just before he reaches Jane. You can ignore air resistance and the mass of the vine.


Homework Equations


K_1 + U_1= K_2 + U_2

h= ((v_0)^2(sin^2))/(2g)



The Attempt at a Solution



i don't know how to relate the angles with this problem?
 
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  • #2
i don't know how to relate the angles with this problem?
Then don't worry about it. Just try to solve the problem.


Incidentally, where did

h= ((v_0)^2(sin^2))/(2g)

come from? (sin^2) doesn't even make sense!


(Okay, technically it does make sense, but you almost certainly did not mean what that expression means)
 
  • #3
Draw a vertical line on piece a paper. Then draw an intersecting line downward and to the left at an angle of 45 degrees to the original line. Then draw another line outward from the same intersection point downward and to the right at 30 degrees to the original line. Now the pivot point for the vine is where the lines intersect and Tarzan swings on the vine in a circular path on a 20m long vine from the 45 degree line to the 30 degree line. So figure out the change in height, and calculate the kinetic energy from the change in potential energy.
 

1. What is gravitational potential energy?

Gravitational potential energy is the energy that an object possesses due to its position in a gravitational field. It is the energy that is required to move an object from one position to another within the gravitational field.

2. How is gravitational potential energy of Tarzan calculated?

The gravitational potential energy of Tarzan can be calculated using the formula PE = mgh, where m is the mass of Tarzan, g is the acceleration due to gravity, and h is the height from which Tarzan is swinging.

3. Why is Tarzan able to swing higher as he gains height?

As Tarzan gains height, he also gains potential energy. This potential energy is then converted into kinetic energy as he swings down, allowing him to swing higher and higher with each swing.

4. Does Tarzan's mass affect his gravitational potential energy?

Yes, Tarzan's mass does affect his gravitational potential energy. The greater his mass, the greater his potential energy will be. This means that a heavier Tarzan will have a higher potential energy than a lighter Tarzan.

5. How does the height from which Tarzan swings affect his gravitational potential energy?

The higher Tarzan swings from, the greater his potential energy will be. This is because as the height increases, so does the distance from the ground, resulting in a higher gravitational potential energy.

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