Homework Problems

1	(a) A ball is thrown straight up with velocity v. Find an equation for the height to which it rises. (b) Generalize your equation for a ball thrown at an angle θ above horizontal, in which case its initial velocity components are vx = v cos θ and vy = v sin θ.
2	At the Salinas Lettuce Festival Parade, Miss Lettuce of 1996 drops her bouquet while riding on a float moving toward the right. Compare the shape of its trajectory as seen by her to the shape seen by one of her admirers standing on the sidewalk.
3	Two daredevils, Wendy and Bill, go over Niagara Falls. Wendy sits in an inner tube, and lets the 30 km/hr velocity of the river throw her out horizontally over the falls. Bill paddles a kayak, adding an extra 10 km/hr to his velocity. They go over the edge of the falls at the same moment, side by side. Ignore air friction. Explain your reasoning. (a) Who hits the bottom first? (b) What is the horizontal component of Wendy's velocity on impact? (c) What is the horizontal component of Bill's velocity on impact? (d) Who is going faster on impact?
4	A baseball pitcher throws a pitch clocked at vx = 73.3 mi/h. He throws horizontally. By what amount, d, does the ball drop by the time it reaches home plate, L = 60.0 ft away? (a) First find a symbolic answer in terms of L, vx, and g. (b) Plug in and find a numerical answer. Express your answer in units of ft. [Note: 1 ft=12 in, 1 mi=5280 ft, and 1 in=2.54 cm]
5	A cannon standing on a flat field fires a cannonball with a muzzle velocity v, at an angle θ above horizontal. The cannonball thus initially has velocity components vx = v cos θ and vy = v sin θ. (a) Show that the cannon's range (horizontal distance to where the cannonball falls) is given by the equation R = (2v2/g) sin θ cos θ . (b) Interpret your equation in the cases of θ = 0 and θ = 90 °.	Solution, p. 280
6	Assuming the result of problem 5 for the range of a projectile, R = (2v2/g) sin θ cos θ, show that the maximum range is for θ = 45 °.	∫
7	Two cars go over the same bump in the road, Maria's Maserati at 25 miles per hour and Park's Porsche at 37. How many times greater is the vertical acceleration of the Porsche? Hint: Remember that acceleration depends both on how much the velocity changes and on how much time it takes to change.	√