Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

(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 v_{x} =
v cos θ and v_{y} = 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 v_{x} = 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, v_{x}, 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 v_{x} = v cos θ and v_{y} = v sin θ.
(a) Show that the cannon's range (horizontal distance to where the
cannonball falls) is given by the equation R = (2v^{2}/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 = (2v^{2}/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.