EXAM I, PHYSICS 1403
July 14, 2004
Dr. Charles W. Myles
INSTRUCTIONS: Please read ALL of these before doing anything else!!!
1. PLEASE put your name on every sheet of paper you use and write on one side of the paper
only!! PLEASE DO NOT write on the exam sheets, there will not be room! Yes, this wastes
paper, but it makes my grading easier!
2. PLEASE show all work, writing the essential steps in the solutions. Write appropriate
formulas first, then put in numbers. Partial credit will be LIBERAL, provided that essential
work is shown. Organized, logical, easy to follow work will receive more credit than
disorganized work.
3. The setup (PHYSICS) of a problem will count more heavily than the math of working it out.
4. PLEASE write neatly. Before handing in your solutions, PLEASE: a) number the pages and
put the pages in numerical order, b) put the problem solutions in numerical order, and c)
clearly mark your final answers. If I can’t read or find your answer, you can't expect me to
give it the credit it deserves.
NOTE: I HAVE 61 EXAMS TO GRADE!!! PLEASE HELP ME
GRADE THEM EFFICIENTLY BY FOLLOWING THE ABOVE
SIMPLE INSTRUCTIONS!!! FAILURE TO FOLLOW THEM
MAY RESULT IN A LOWER GRADE!! THANK YOU!!
An 8.5’’ x 11’’ piece of paper with anything written on it and a calculator are allowed.
NOTE: Problem 1 consists of Conceptual Questions and IS REQUIRED! You may
work any three (3) of the remaining four problems for four (4) problems total for this
exam. Each problem is equally weighted and worth 25 points, for a total of 100 points on
this exam.
1. THIS PROBLEM IS MANDATORY!!! CONCEPTUAL QUESTIONS: Answer
these briefly in a few complete and grammatically correct English sentences.
a. By using a ball thrown straight up into the air as an example, explain the error in
the common misconception that acceleration and velocity are always in the same
direction.
b. Explain the error in the common misconception that an object thrown upward has
zero acceleration at its highest point. (What would happen if that were true?)
c. See figure! A child sits in a wagon, which is moving to the right
(x-direction) at constant velocity v0x. She throws an apple straight
up (from her viewpoint) with an initial velocity v0y while she
continues to travel forward at v0x. Neglect air resistance. Will the
apple land behind the wagon, in front of the wagon, or in the
wagon? WHY? Explain (briefly!) your answer. (Use what you know about
projectiles!). Make a sketch of the situation to illustrate your explanation.
d. For 5 BONUS POINTS, answer the following question: During our class
discussion about projectiles, I did an in-class demonstration which illustrates the
answer to this question about the child in the wagon. Briefly describe this
demonstration. (If you were in class the day I did this demonstration, you probably will
be able to answer this. However, if you “cut” class that day, as several of you are already
in the habit of doing, you probably won’t be able to answer it!)
NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!!
2. See figure. At time t = 0, a car is at the origin and is traveling at a velocity of 45 m/s
along the positive x-axis. It is undergoing a constant acceleration in the negative xdirection, so it is slowing down. At t = 15 s after it has passed the origin, it has
a
slowed down to 20 m/s.
a. Compute the acceleration of the car.
t=0
v0
v0 = 45 m/s
b. How far has the car moved in the 15 s?
t = 15 s
c. Assuming that the acceleration remains constant,
v = 20 m/s
compute the car’s velocity at time t = 20 s after it
has passed the origin.
d. Assuming that the acceleration remains constant, how far past the origin does the
car stop?
e. Assuming that the acceleration remains constant, how long after it passes the
origin does it take the car to stop?
3. See figure. The following takes place on the Klingon home planet. On that
planet, the acceleration due to gravity is g = 7.0 m/s2. (Note: This means
DO NOT use g = 9.8 m/s2 in what follows!!). A Klingon throws a
ball upward into the air with an initial velocity of 20 m/s. It goes up and
eventually comes back down. Assume vertical motion only and neglect air
resistance in what follows.
a. What are the ball’s acceleration and velocity at the top of its flight?
b. Compute the maximum height the ball reaches.
c. How long does it take the ball to reach the maximum height? How long
does it take the ball to make one complete round trip and come back to
the Klingon’s hand?
d. Compute ball’s velocity (magnitude and direction) when it reaches the person’s
hand again.
e. For 5 BONUS POINTS, compute the times at which the ball passes a point 10 m
above the ground. (Hint: To answer this you will have to solve a quadratic
equation using the quadratic formula!)
v
NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5
4. See figure. An Alaskan rescue plane drops a package
of emergency rations to stranded hikers, as shown. The
plane is traveling HORIZONTALLY at a constant
velocity v0 = 40 m/s. at a height of 100 m above the
ground. To solve the following, take the origin (x0 = y0
= 0) at the position of the plane when it drops the
package.
a. Compute the time it takes the package to reach the
ground.
b. Compute the horizontal distance at which the
package strikes the ground, relative to the point at
which it is released. (That is, compute the x
distance it lands, measured from a point directly
above where the plane drops it).
c. Compute the horizontal and vertical components of
the package velocity just before it hits.
d. Use the results of part c. to compute the magnitude of the package’s final velocity
and the angle the final velocity vector makes with the horizontal.
e. Compute time at which the package passes a point 50 m above the ground and the
horizontal distance it has moved at that time.
5. See figure. A plane is heading due East at a
constant velocity, with respect to still air, of
vPA = 350 km/h. A wind begins blowing
from the Northeast (towards the Southwest)
at a constant velocity of vAG = 60 km/h.
NOTE: You do NOT need to convert km/h
to m/s to do this problem! Use the analytic
(trigonometric) method to do the required
vector addition in what follows, NOT the
graphical method.
a. Make a sketch of the situation and label
it with appropriate quantities.
b. Compute the components of the resultant velocity of the plane with respect to the
ground, vPG, along the East-West axis and along the North-South axis.
c. Compute the magnitude and direction (with respect to the x-axis) of the resultant
velocity, vPG, of the plane with respect to the ground.
d. After the wind has been blowing for 0.75 hour, if the pilot has taken no corrective
action, compute the component of the plane’s displacement along the East-West
axis and the component of this displacement along the North-South axis.
e. Use the results of part d. to compute the magnitude and direction of the total
displacement of the plane 0.75 hour after the wind starts blowing (if the pilot
takes no corrective action).