Tarzan, mass 85 kg, swings down on the end of a 28 m vine from a tree limb 4.4 m above the ground. How fast is Tarzan moving when he reaches the ground?
Use energy conservation.
M g H = (1/2) M V^2
V = sqrt (2gH)
H is the vertical distance that he falls, 4.4 m.
g = 9.8 m/s^2
His mass will not matter. It cancels out.
a car increases its speed from 50km/hr to 75km/hr in 15mintues. what is the acceleration of the car
To find how fast Tarzan is moving when he reaches the ground, we can use the principle of conservation of energy. The initial potential energy of Tarzan is converted into kinetic energy as he swings down.
Let's calculate the potential energy and the kinetic energy for Tarzan:
Potential Energy (PE) = m * g * h
where m is the mass of Tarzan, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the tree limb.
PE = 85 kg * 9.8 m/s^2 * 4.4 m
PE = 3642.8 J
Kinetic Energy (KE) = (1/2) * m * v^2
where v is the velocity of Tarzan when he reaches the ground.
KE = (1/2) * 85 kg * v^2
According to the principle of conservation of energy, the potential energy at the top (PE) is equal to the kinetic energy at the bottom (KE).
PE = KE
3642.8 J = (1/2) * 85 kg * v^2
7285.6 J = 85 kg * v^2
Now, let's solve for v:
v^2 = 7285.6 J / 85 kg
v^2 = 85.6 m^2/s^2
Taking the square root of both sides, we get:
v = √(85.6 m^2/s^2)
v ≈ 9.26 m/s
Therefore, Tarzan is moving at approximately 9.26 m/s when he reaches the ground.
To calculate Tarzan's speed when he reaches the ground, we can use the laws of conservation of energy and the principle of energy conversions.
First, let's determine the potential energy (PE) Tarzan has when he swings from the vine at the starting height. The potential energy can be calculated using the formula:
PE = m * g * h
where m is the mass of Tarzan, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height (4.4 m).
PE = 85 kg * 9.8 m/s² * 4.4 m
PE = 3611.6 Joules
At the starting point, Tarzan's potential energy is fully converted into kinetic energy (KE) at the lowest point of the swing. So, we equate the potential energy to the kinetic energy:
PE = KE
KE = 3611.6 Joules
The formula for kinetic energy is:
KE = (1/2) * m * v²
where v is the velocity of Tarzan when he reaches the ground.
Rearranging the equation to solve for v:
v² = (2 * KE) / m
v = √((2 * KE) / m)
Substituting the values:
v = √((2 * 3611.6 Joules) / 85 kg)
v ≈ √84.97 m²/s²
v ≈ 9.2 m/s
Therefore, Tarzan is moving at a speed of approximately 9.2 m/s when he reaches the ground.