1. A cannon is fired from a castle wall at some unknown height above the ground. The can- nonball leaves the cannon with speed 30.0m/'s at angle 30% above the horizontal and hits the level ground at a horizontal distance 100m from the wall. a) Calculate the time it takes the cannon ball to hit the ground. b) Calculate the height of the castle wall. c) What are the x- and y-components of the cannon ball's velocity at the highest point of its trajectory? d) What are the x- and y-components of the cannon ball's velocity just before it hits the ground? e) Sketch, qualitatively, x-t, yet, va-t and vy-t graphs for the cannon ball's motion. 2. A kangaroo jumping across flat ground is leaving the ground at an angle 0=30' with respect to the horizontal and lands a horizontal distance 10.0m from its takeoff point. Find the kangaroo's initial speed. 3. In a lecture demonstration, the instructor aims a blow gun directly at Barney, a stuffed purple dinosaur, who is suspended from the ceiling at a vertical height # above the muzzle of the blow gun, a horizontal distance D away. At the instant she launches a dart with speed vo and angle 0 above the horizontal, Barney is released from rest. a) Derive an expression, in terms of D, vo and @, for the time / it takes the dart to cover the hori- zontal distance D. H A b) Derive an expression, in terms of system parameters, for the dart's vertical position yo when the dart has covered the horizontal distance D. Use the expression for 7 you found in a). c) Derive an expression, in terms of system parameters, for Barney's vertical position ys at the instant the dart has the covered horizontal distance D. Use the expression for / you found in a). d) Compare ys and yo. (Hint: aiming the blow gun directly at Barney means that D, A and 0 are related!)