## Activity Based Physics Thinking Problems in Mechanics: Projectile Motion |

- (a) The gravitational force
- (b) The time it will take to fall a given distance in air
- (c) The time it will take to fall a given distance in vacuum
- (d) The total force on the object when falling in vacuum
- (e) The total force on the object when falling in air.
- What is the physical system being described by this equation?
- What does each symbol represent?
- Under what conditions does the equation hold?
1) A boy and a girl are tossing an apple back and forth between them. The sketch at the right shows the path the apple followed when watched by an observer looking on from the side. The apple is moving from the left to the right. Five points are marked on the path. Ignore air resistance. (a) Make a copy of this figure. At each of the marked points, draw an
arrow that indicates the magnitude and direction of the apple's velocity
when it passes through that point. 2) Student A says: Galileo said all objects fall with the same speed. I know that's not true. If I drop a balloon and a billiard ball the balloon falls more slowly. Galileo was wrong. Student B says: No. Galileo only said two heavy objects fall with the same speed. If I drop a steel ball and a wooden ball they hit the ground at the same time. Discuss these student's statements. Which one do you agree with? If either or both are wrong, explain why. 3) Consider a metal sphere two inches in diameter (S) and a feather (F). For each quantity in the list below indicate the relation between the quantity for S and F. Is it the same, greater, or lesser? Explain in each case why you gave the answer you did. 4) In C. S. Forster's novel Lieutenant Hornblower (set in the early
1800's) a British naval vessel tries to sneak by a Spanish garrison. The
ship passes as far away from the Spanish guns as it can -- a distance s.
The Spanish gunner knows that his gun has a muzzle velocity equal to v (a) Once the gun is fired, what controls the motion of the cannonball?
Write the equations that determine the vector acceleration of the cannonball
after it leaves the cannon. You may ignore air resistance. You may need one of the following trigonometric identities (true for
all angles theta): 5) A golfer is trying to hit a golf ball onto the green. The green is
a horizontal distance s from his tee and it is up on the side of a hill
a height h above his tee. When he strikes the ball it leaves the tee at
an angle theta to the horizontal. He wants to know with what speed, v (a) Once he has struck the ball, what controls its motion? Write the
equations that determine the vector acceleration of the golf ball after
it leaves the tee. Be sure to specify your coordinate system. For this
part of the problem you may ignore air resistance. 6) The Baltimore Orioles are playing the Boston Red Sox at Fenway Park in Boston. Cal Ripken hits a long fly ball. The ball left his bat at a speed V at an angle of theta above the horizontal. The ball heads towards the "Green monster" in left field -- a high fence. The fence is a distance s from Ripken at home plate and its height is h. (a) Draw a labeled diagram of what is happening. 7) A test rocket containing a probe to determine the composition of the upper atmosphere is fired vertically upward from an initial position at ground level. During the time T while its fuel supply lasts, it ascends with a constant upward acceleration of magnitude 2g. Assume that air resistance can be neglected and that the rocket goes a small enough height that the earth's gravitational force can be assumed to be constant. (a) What is the speed and height of the rocket above ground level when
the fuel runs out?
9) In our readings about mechanics we encounter the following equations: For each equation, discuss the following questions. Sketch on your paper a diagram in which you put each of the equations in a box. Connect with an arrow any pair of equations when one equation can be easily derived from another by considering a special case. (The arrow should point from the more general to the more specific equation.) |

These problems written and collected by E. F. Redish. Photos and figures
by E. F. Redish. These problems may be freely used in classrooms. They
may be copied and cited in published work if the *Activity Based Physics
Thinking Problems in Physics site* is mentioned and the URL given. Web
page edited by K.A. Vick

To contribute problems to this site, send them to redish@physics.umd.edu.

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Last modified June 21, 2002