With what speed must the rocket have left the cannon in order to just reach the drone ship?
From time to time, somebody comes up with the idea of launching objects into space using a giant cannon rather than a rocket. Earth’s atmosphere makes this hard since drag forces get in the way, but let’s have a bit of fun and pretend that Earth has no atmosphere so that we can at least consider the possibility. In particular, imagine using a cannon to send a SpaceX Falcon 9 rocket 613 km downrange to land on a ship in the ocean. Assume the rocket is fired at an angle of 45 degrees above horizontal, and that its initial velocity is entirely provided in one burst by the cannon (an actual rocket has engines which burn and therefore provide acceleration for a longer period of time).
Here are the questions of interest for this hypothetical situation:
With what speed must the rocket have left the cannon in order to just reach the drone ship? Give your answer in units of km/hr.
If the cannon was 1 km long, what acceleration is required for the rocket to reach its launch speed by the time it leaves the barrel of the cannon? Give your answer in units of g, where 1 g = 9.8 m/s2 is the magnitude of the acceleration due to gravity near the surface of Earth. Do you think this would be a viable method for transporting people around the Earth? Explain.
Now that you’ve seen the circular “windmill” motion of the arm during a pitch, you’re ready to use the knowledge you’ve acquired and skills you’ve developed so far in this class to estimate the maximum speed that a human can throw a pitch using this motion without injuring their arm. The actual maximum speed of a fastpitch softball pitch is between 75 and 100 mph. In the discussion of your analysis, be sure to compare your estimates to these actual values. If your estimate differs from the actual maximum speed (which it very well might!), discuss what this tells you about the pitching motion.
All estimates must be based upon the physics model of a human throwing a “windmill” pitch that you’ve created and must be calculated using this model. You may find it useful to know the following facts:
The greatest weight a human has lifted off the ground using two arms (i.e., an unaided “deadlift” in which weight is lifted vertically upwards with both arms extended below) is around 1000 pounds (see the Wikipedia article on the deadlift (Links to an external site.) for details). You might find it useful to use this (or a quantity derived from it) as your estimate of the maximum force that can be exerted by a human arm without injury.
A softball has a mass of approximately 200 g.
Create a single page document (e.g., a Google Doc) on which you show all of your relevant work. If you’d like to do some work by hand on paper, you may do that and paste an image into your document (just make sure your handwriting is easy to read). I encourage you to include typed text on the document as well to justify your choices and thoroughly explain how you arrived at your quantitative estimates. Once you’ve done that, export a single-page PDF of your document (as you’ve done for labs) and submit it.