AJM:12/14/01 Score /100
Physics 13101 First Midterm Exam Winter 2000
Name
PLEASE READ THIS FIRST: Work the problems on separate sheets of paper and staple this sheet to the
front. Read each problem carefully. Show your work and/or give explanations for all answers. Make sure
that all numerical answers are given with a reasonable number of sig figs and that you have included
appropriate units. Check your answers for physical reasonableness whenever possible. I do give partial
credit, but only if I can follow your work, so be as clear as possible about what you are doing.
1. [25 pts] In order to pass another car, you increase your speed from 20 m/s to 30 m/s in 5.0 s.
Assuming the acceleration is constant, how far do you travel during that time?
2. A friend is stranded on a small ledge part way up a vertical cliff and she is getting very hungry. In an
attempt to help, you make her a peanut butter and jelly sandwich and use a very special “sandwich
gun” to shoot it to her. You stand 300 m away from the base of the cliff, aim the gun 60° above the
horizontal, and launch the sandwich with an initial speed of 80 m/s. Incredibly, the sandwich is not at
all affected by air resistance (!!) and its trajectory takes it directly to your friend.
a) [15 pts] How high up the cliff was your friend?
b) [10 pts] When the sandwich reached your friend, was it still gaining altitude or was
it falling from the peak of its trajectory?
c) [10 pts, extra credit] If you had launched the sandwich at an angle of 45° above the
horizontal (toward the same ledge and from the same position), what initial speed
would have been required?
3. As shown at right, a fly starts out (at t = 0) at a position ri = 4.0
m, west relative to a spider (who defines the “origin”), and flying
with an initial velocity
vi = 1.5 m/s, north. During the next 2.0 s it maintains an
acceleration a = 3.0 m/s2, 30° east of south.
a) [5 pts] At t = 0, is the fly’s speed increasing or
decreasing? As always, explain.
b) [5 pts] Since a is constant, the fly’s final position is
given by the vector sum rf = ri + vit + 1
2 at2. Find the two vectors vit and 1
2 at2 and
then draw a reasonably accurate diagram that graphically shows the vector sum.
c) [15 pts] Find the fly’s final position rf (magnitude and direction)—i.e., do the sum!
4. A race car is traveling at 70 m/s (~157 mph) and has an acceleration of magnitude 10 m/s2 (~ 1 g) that
forms a right angle with the instantaneous velocity.
a) [10 pts] Describe the current path of the car in detail including at least one
important descriptive quantity that you can calculate numerically.
b) [10 pts] Assuming that the car never speeds up or slows down and that 10 m/s2 is
the maximum magnitude of the acceleration that can be attained (as a result of
limited friction between the tires and the road), what is the minimum time for it to
complete a single lap around the race course?
r
i
a
v
i
spider
North
fly
