Tarzan is standing on a 20m high cliff and swings on a vine to the jungle floor below. How fast is Tarzan swinging when he reaches the jungle floor?
To determine Tarzan's swinging speed when he reaches the jungle floor, we can use the principle of conservation of energy.
First, let's assume there is no air resistance or friction to simplify the problem.
We can consider the initial and final energy of Tarzan. Initially, when Tarzan is standing on the cliff, he has gravitational potential energy which is given by the formula:
PE_initial = m * g * h
Where:
PE_initial = initial potential energy (Joules)
m = mass of Tarzan (Assume it's 70 kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height of the cliff (20 m)
So, PE_initial = 70 kg * 9.8 m/s^2 * 20 m = 13,720 J
When Tarzan reaches the jungle floor, all his potential energy is converted into kinetic energy as he swings down. The formula for kinetic energy is:
KE_final = (1/2) * m * v^2
Where:
KE_final = final kinetic energy (Joules)
m = mass of Tarzan (Assumed to be 70 kg)
v = velocity of Tarzan when he reaches the jungle floor (m/s)
Since energy is conserved, the initial potential energy is equal to the final kinetic energy:
PE_initial = KE_final
13,720 J = (1/2) * 70 kg * v^2
Simplifying the equation further:
v^2 = (2 * PE_initial) / m
v^2 = (2 * 13,720 J) / 70 kg
v^2 = 23,782.86 J/kg
Taking the square root of both sides to solve for v:
v = sqrt(23,782.86 J/kg) ≈ 154.1 m/s
Therefore, Tarzan is swinging at approximately 154.1 m/s when he reaches the jungle floor.