Question

Tarzan, in one tree, sights Jane in another tree. He grabs the end of a vine with length 11 m that makes an angle of 45∘ 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∘ with the vertical. Determine whether he gives her a tender embrace of knocks her off her limb by calculating Tarzan's speed just before he reaches Jane. You can ignore air resistance.

Answer 1

1.75 m/s

Step-by-step explanation:

length of the vine (L) = 11 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 = (11 - 11cos45) - (11 - 11cos30) = 3.2 m

v =
`√(2×9.8×)`

v = 1.75 m/s