King Kong carries Fay Wray up the 321 m tall Empire State Building. At the top of the skyscraper, Fay Wray’s shoe is knocked off with an initial upwards velocity of 5.1 and falls towards the ground.
With what final velocity will the shoe be moving when it hits the ground?
Vfinal^2 - Vinitial^2 = 2 g H
H = 321 m
You should have provided dimensions for the upward velocity. I assume it is m/s.
To solve for the final velocity of the shoe when it hits the ground, we can use the principle of conservation of energy.
First, let's determine the potential energy of the shoe at the starting point and the kinetic energy of the shoe when it hits the ground.
1. Potential Energy at the starting point:
The potential energy is given by the formula: PE = m * g * h
Where:
m = mass of the shoe (which we'll assume to be 1 kg for simplicity)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height of the building (321 m)
PE = 1 kg * 9.8 m/s^2 * 321 m
PE = 3150.78 J
2. Kinetic Energy at the end point:
The kinetic energy is given by the formula: KE = (1/2) * m * v^2
Where:
m = mass of the shoe (1 kg)
v = final velocity of the shoe when it hits the ground
Since the shoe is falling, it does not have any initial kinetic energy. Therefore, all of the potential energy at the starting point will be converted into kinetic energy at the end point.
PE = KE
3150.78 J = (1/2) * 1 kg * v^2
Solving for v^2:
v^2 = (2 * 3150.78 J) / 1 kg
v^2 = 6301.56 m^2/s^2
Finally, taking the square root of both sides to find v:
v = sqrt(6301.56 m^2/s^2)
v ≈ 79.4 m/s
Therefore, the final velocity of the shoe when it hits the ground will be approximately 79.4 m/s.
To determine the final velocity of the shoe when it hits the ground, we need to use the equation for free fall motion. This equation is given by:
v^2 = u^2 + 2as
where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration due to gravity (approximately 9.8 m/s^2)
- s is the displacement (change in height)
In this case, the initial velocity (u) of the shoe is 5.1 m/s downwards (as it is knocked off with an upwards velocity), the acceleration due to gravity (a) is 9.8 m/s^2 downwards, and the displacement (s) is the height of the Empire State Building, which is 321 meters.
Plugging these values into the equation, we have:
v^2 = (5.1 m/s)^2 + 2 * (9.8 m/s^2) * (321 m)
Now we can calculate the final velocity:
v^2 = 26.01 m^2/s^2 + 6291.36 m^2/s^2
v^2 ≈ 6317.37 m^2/s^2
Taking the square root of both sides to find the final velocity:
v ≈ √(6317.37 m^2/s^2)
v ≈ 79.51 m/s
Therefore, the shoe will be moving with a final velocity of approximately 79.51 m/s when it hits the ground.