As a science project, you drop a watermelon off the top of the Empire State Building, 320 m above the sidewalk. It so happens that Superman flies by at the instant you release the watermelon. Superman is headed straight down with a speed of 36.0 m/s. How fast is the watermelon going when it passes Superman?
Well, they have traveled the same distance in the same time.
It is rather simple. The only way the same distance in the same time can happen if they have the same average velocity. The average velocity of the superman is 36, the watermellon started at zero, so it is at 72m/s at the finish (to give it an average velocity at 36)
I am most certain there are much more complicated ways of solving this.
To solve this problem, we can make use of the conservation of energy principle.
Step 1: Determine the initial potential energy of the watermelon at the top of the building.
The potential energy of an object near the surface of the Earth is given by the equation:
Potential energy = mass * acceleration due to gravity * height
Given that the watermelon is at a height of 320 m and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the initial potential energy:
Potential energy = mass * 9.8 m/s^2 * 320 m
Step 2: Determine the initial kinetic energy of the watermelon.
Since the watermelon is initially at rest, its initial kinetic energy is zero.
Step 3: Determine the final potential energy of the watermelon at the level of Superman.
When the watermelon reaches the level of Superman, its height above the ground will be 320 m - [(time for the watermelon to reach Superman) * (Superman's downward velocity)].
Step 4: Determine the final kinetic energy of the watermelon at the level of Superman.
Since the watermelon is still falling, all of its initial potential energy will be converted into kinetic energy. Therefore, the final potential energy will be zero.
Step 5: Equate the initial potential energy to the final kinetic energy and solve for the final velocity of the watermelon using the equation:
Final kinetic energy = 0.5 * mass * (final velocity)^2
Final velocity = √(2 * initial potential energy / mass)
Note: In this problem, we are assuming that air resistance is negligible.
Therefore, you need to know the mass of the watermelon to solve for the final velocity.
To solve this problem, we need to analyze the motion of both the watermelon and Superman separately. We will use the laws of motion and equations of motion to determine the final velocity of the watermelon when it passes Superman.
Let's start by analyzing the motion of the watermelon. We know that the watermelon is dropped from rest, so its initial velocity is 0 m/s. The acceleration due to gravity, denoted as "g," is approximately 9.8 m/s^2, as it acts downward.
Using the equation of motion:
v² = u² + 2as,
where:
v = final velocity,
u = initial velocity,
a = acceleration, and
s = displacement,
we can find the final velocity of the watermelon when it reaches Superman.
Since the watermelon is dropped from a height of 320 m, and it falls freely under the influence of gravity, the displacement (s) is 320 m, the acceleration (a) is -9.8 m/s^2 (negative because it acts downward), and the initial velocity (u) is 0 m/s.
Plugging these values into the equation of motion, we get:
v² = (0)² + 2(-9.8)(320)
v² = 0 + (-6272)
v² = -6272
We have a negative value, which indicates that the velocity is in the downward direction. However, in this case, we are interested in the magnitude of the velocity, so we ignore the negative sign. Therefore:
v = √(6272)
v ≈ 79.24 m/s
So, when the watermelon passes Superman, its velocity is approximately 79.24 m/s.
Note: It is important to keep in mind that this analysis assumes ideal conditions and neglects factors such as air resistance, Superman's effect on the watermelon, and the specific mechanics associated with comic book characters.