Tarzan swings on a 33.0-m-long vine initially inclined at an angle of 39.0 degre

Question

Tarzan swings on a 33.0-m-long vine initially inclined at an angle of 39.0 degree with the vertical. What is his speed at the bottom of the swing if he starts from rest? What is his speed at the bottom of the swing if he pushes off with a speed of 5.00 m/s? A skier of mass 79 kg is pulled up a slope by a motor-driven cable. How much work is required to pull him 90 m up a 30 degree slope (assumed frictionless) at a constant speed of What power (expressed in hp) must a motor have to perform this task?

Explanation / Answer

given,

length of vine = 3.3 m

angle = 39 degree

by conservation of energy

mg * (33 - 33 * cos(39)) = 0.5 * mv^2

g * (33 - 33 * cos(39)) = 0.5 * v^2

v = 12.0059 m/s

if he gets push of 5 m/s then

g * (33 - 33 * cos(39)) + 0.5 * 5^2 = 0.5 * v^2

v = 13.0055 m/s

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