You decide you are done with physics and you run away to join a local 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. They plan to shoot the person out of the cannon from off the train and just before they land, a trapeze artist will swoop them up before they get hit by the train. The Ringmistress of the circus learns that you used to be a physicist 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 $v_0$ and launch angle $ heta$. At the moment they launch, the train which had been moving with speed $v_{train}$, 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 cannonball's velocity in the ground reference frame and find the time of flight for the projectile. c. Using the result from part b, and your knowledge of kinematics, 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)? 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.