1. You decide you are done with physics and you run away to join a traveling circus. The circus is putting on a new act which involves launching someone out of a cannon, “the human cannonball," however, the cannon is mounted atop a train. The human cannonball will be launched forward from atop the train, just before landing in front of the train, a trapeze artist will swoop them up before they get hit by the train. The Ring Mistress of the circus learns that you studied physics and decides she wants you to do some calculations for the safety of the human cannonball. You can't seem to escape your physics class even in the circus. Suppose the human cannonball is launched with speed v, and launch angle 0. At the moment they launch, the train which had been moving with speed verain, begins to accelerate with acceleration a d. Find an expression for the angle at which the human cannonball should be fired so that they land as far as possible away from the accelerating train. (Hint: some calculus is involved in this step. From your calculus classes, how do you maximize a quantity?) e. Asses the validity of your work. Is this what you expected, does the answer make physical sense? Does your expression have the correct units? What is the maximal range of a projectile in a stationary frame (do not calculate this, it's in the book)? Check some limiting cases such as when a < 0, a > 0, and a = 0? Compare to the stationary frame. Do the results make sense?
1. You decide you are done with physics and you run away to join a traveling circus. The circus is putting on a new act which involves launching someone out of a cannon, “the human cannonball," however, the cannon is mounted atop a train. The human cannonball will be launched forward from atop the train, just before landing in front of the train, a trapeze artist will swoop them up before they get hit by the train. The Ring Mistress of the circus learns that you studied physics and decides she wants you to do some calculations for the safety of the human cannonball. You can't seem to escape your physics class even in the circus. Suppose the human cannonball is launched with speed v, and launch angle 0. At the moment they launch, the train which had been moving with speed verain, begins to accelerate with acceleration a d. Find an expression for the angle at which the human cannonball should be fired so that they land as far as possible away from the accelerating train. (Hint: some calculus is involved in this step. From your calculus classes, how do you maximize a quantity?) e. Asses the validity of your work. Is this what you expected, does the answer make physical sense? Does your expression have the correct units? What is the maximal range of a projectile in a stationary frame (do not calculate this, it's in the book)? Check some limiting cases such as when a < 0, a > 0, and a = 0? Compare to the stationary frame. Do the results make sense?
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Transcribed Image Text:1. You decide you are done with physics and you run away to join a traveling circus.
The circus is putting on a new act which involves launching someone out of a
cannon, “the human cannonball," however, the cannon is mounted atop a train. The
human cannonball will be launched forward from atop the train, just before landing in
front of the train, a trapeze artist will swoop them up before they get hit by the train.
The Ring Mistress of the circus learns that you studied physics and decides she wants
you to do some calculations for the safety of the human cannonball. You can't seem
to escape your physics class even in the circus. Suppose the human cannonball is
launched with speed vo and launch angle 0. At the moment they launch, the train
which had been moving with speed verain, begins to accelerate with acceleration a
d. Find an expression for the angle at which the human cannonball should be fired so
that they land as far as possible away from the accelerating train. (Hint: some calculus
is involved in this step. From your calculus classes, how do you maximize a quantity?)
e. Asses the validity of your work. Is this what you expected, does the answer make
physical sense? Does your expression have the correct units? What is the maximal
range of a projectile in a stationary frame (do not calculate this, it's in the book)?
Check some limiting cases such as when a < 0, a > 0, and a = 0? Compare to the
stationary frame. Do the results make sense?
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