Watermelon and Superman experiment

[BMWPower06]

Homework Statement

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 32.0.

How fast is the watermelon going when it passes Superman?

Homework Equations

Vf=Vi+at
X=Vit+(1/2)at^2

The Attempt at a Solution

I guess you have to figure the velocity of the watermelon first correct? But I'm not certain how to do that. And, once I figure out the watermelon's velocity how do I determine when it passes superman?

 

[matt-83]

You are going to want to find out how far above the sidewalk Superman is when the Watermelon passes him.

To do this set the equation that shows Superman's displacement (x=vt) equal to the equation for the watermelon's displacement (X=Vit+(1/2)at^2). You can do this because the displacement for both Superman and the watermelon will be equal when they are passing.

 

[thomate1]

I would approach this experiment by first considering the forces acting on the watermelon and Superman. The watermelon is initially at rest and will experience a downward force due to gravity. Superman, on the other hand, is flying downwards with a constant velocity, meaning he is not accelerating and therefore not experiencing any net force.

Using the equations provided, we can calculate the watermelon's velocity as it falls. We know the initial velocity (Vi) is 0 m/s, the acceleration (a) is 9.8 m/s^2 (due to gravity), and the distance (X) is 320 m. By plugging these values into the equation X=Vit+(1/2)at^2 and solving for Vf, we find that the watermelon's velocity when it reaches the sidewalk is approximately 80 m/s.

Now, to determine when the watermelon passes Superman, we need to consider their relative positions and velocities. Since Superman is flying downwards with a constant velocity, we can assume that he will be at the same position (320 m above the sidewalk) when the watermelon reaches that point. Therefore, we can say that the watermelon passes Superman when it reaches a velocity of 32 m/s, which is equal to Superman's velocity.

In conclusion, the watermelon's velocity when it passes Superman is approximately 80 m/s, and this occurs when the watermelon has fallen 320 m and has a velocity equal to Superman's. This experiment demonstrates the principles of gravity and relative motion, and can be used to further explore these concepts in a scientific setting.