tarzan, mass 85 kg, swings from a tree on the end of a 20. m vine his feet touch the ground 4.0m below the tree. how fats was he moving when he reaches the ground
(1/2) m v^2 = m g h
so
v = sqrt (2 g h) = sqrt (2*9.81*4)
To determine Tarzan's speed when he reaches the ground, we need to use the principles of conservation of energy. We can consider the initial gravitational potential energy of Tarzan at the top of the swing and his final kinetic energy at the bottom of the swing.
The initial gravitational potential energy (PE) of Tarzan at the top is given by the equation:
PE = m * g * h
Where:
m = mass of Tarzan = 85 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height from the ground to the top of the swing = 4.0 m
So, the initial potential energy can be calculated as:
PE = 85 kg * 9.8 m/s^2 * 4.0 m
The final kinetic energy (KE) of Tarzan at the bottom of the swing is given by the equation:
KE = (1/2) * m * v^2
Where:
v = velocity of Tarzan at the bottom
Since energy is conserved, the initial potential energy should be equal to the final kinetic energy:
PE = KE
Substituting the equations for PE and KE, we have:
m * g * h = (1/2) * m * v^2
Simplifying the equation, we get:
v^2 = 2 * g * h
Now, we can substitute the known values to find the speed of Tarzan:
v^2 = 2 * 9.8 m/s^2 * 4.0 m
v^2 = 78.4 m^2/s^2
Finally, we take the square root of both sides to find the speed:
v = √(78.4 m^2/s^2)
v ≈ 8.84 m/s
Therefore, Tarzan was moving at approximately 8.84 meters per second when he reached the ground.