Question

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.

Answer 1

v = 7.9 m/s

Step-by-step explanation:

length of the vine (L) = 20 m

initial angle with the vertical = 45 degrees

final angle with the vertical = 30 degrees

acceleration due to gravity (g) = 9.8 m/s^{2}

speed (v) =?

to solve this problem we can apply the equation below:

loss in potential energy = gain in kinetic energy

m x g x h = 1/2 x m x
`v^(2)`

v =
`√(2gh)`

before we can apply the above we need to get our height

height = initial vertical height - final vertical height

height = (L - L cosθ2) - (L - L cosθ1)

height = (20 - 20cos45) - (20 - 20cos30) = 3.2 m

v =
`√(2 x 9.8 x 3.2)`

v = 7.9 m/s