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. NOTE: This problem involves understanding relative motion between the ground's stationary reference frame and the train's moving frame. a. Sketch the physical situation and include any relevant diagrams or information about the problem. List your knowns and unknowns, and any relevant equations. b. Write down the x and y components of the of the cannonball's velocity in the ground reference frame and find the time of flight for the projectile. c. Using the result form part b, and your knowledge of kinematics, to determine the horizontal distance that the projectile travels and the distance the train travels in that time. Given this, what is the range of the human cannonball (i.e. the distance away from the train that the human cannonball will land)?

Question
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
to do some calculations for the safety of the human cannonball. You can't seem
you
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.
NOTE: This problem involves understanding relative motion between the ground's
stationary reference frame and the train's moving frame.
a. Sketch the physical situation and include any relevant diagrams or information
about the problem. List your knowns and unknowns, and any relevant equations.
b. Write down the x and y components of the of the cannonball's velocity in the
ground reference frame and find the time of flight for the projectile.
c. Using the result form part b, and your knowledge of kinematics, to determine the
horizontal distance that the projectile travels and the distance the train travels in that
time. Given this, what is the range of the human cannonball (1.e. the distance away
from the train that the human cannonball will land)?
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 to do some calculations for the safety of the human cannonball. You can't seem you 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. NOTE: This problem involves understanding relative motion between the ground's stationary reference frame and the train's moving frame. a. Sketch the physical situation and include any relevant diagrams or information about the problem. List your knowns and unknowns, and any relevant equations. b. Write down the x and y components of the of the cannonball's velocity in the ground reference frame and find the time of flight for the projectile. c. Using the result form part b, and your knowledge of kinematics, to determine the horizontal distance that the projectile travels and the distance the train travels in that time. Given this, what is the range of the human cannonball (1.e. the distance away from the train that the human cannonball will land)? 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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