Quiz 2, Physics 2a, Oct 2 2010
Double check that you bubble in your code number correctly.
If there’s a mistake, your score will be lowered –as a penalty.
We’re having trouble with people leaving lecture early, causing disruption and loss
of around 10% of our lecture time. If this continues, you’ll find a few questions in future
quizzes that will test attendance in the last few minutes of lectures.
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VERSION A
1. A particle is moving along a path, with position ~r(t). At a certain instant, it is noticed
that
d~
r
dt
6= 0, and also
d2 ~
r
dt2
6= 0, but
d~
r
dt
·
d2 ~
r
dt2
= 0. Which is true at that instant.
(a) The particle is going straight, with changing speed.
(b) The particle is turning direction, but with constant speed.
(c) The particle is turning direction, and speeding up.
(d) The particle is turning direction, and slowing down.
2. The same setup as the previous question. At a different instant, it is noticed that
d~
r
dt
6= 0, and also
d2 ~
r
dt2
instant.
6= 0, but
d~
r
dt
·
d2 ~
r
dt2
< 0 and
d~
r
dt
×
d2 ~
r
dt2
= 0. Which is true at that
(a) The particle is going straight, with changing speed.
(b) The particle is turning direction, but with constant speed.
(c) The particle is turning direction, and speeding up.
(d) The particle is turning direction, and slowing down.
3. The same setup as the previous question. At a different instant, it is noticed that
d~
r
dt
6= 0, and also
instant.
d2 ~
r
dt2
6= 0, but
d~
r
dt
·
d2 ~
r
dt2
< 0 and
d~
r
dt
×
d2 ~
r
dt2
6= 0. Which is true at that
(a) The particle is going straight, with changing speed.
(b) The particle is turning direction, but with constant speed.
(c) The particle is turning direction, and speeding up.
(d) The particle is turning direction, and slowing down.
4. Bruce and Henrietta like playing the game where she “forgets” her bagels, and then
tries to catch them when she’s down on street level. To make the game even more fun,
Bruce now bought a Bagel-BazookaT M , which launches bagels at a maximum velocity
of 50 m/s. He launches the bagels from the window of their apartment, 35 meters
above the ground. He launches them at an angle θ0 = tan−1 ( 43 ) above the horizon.
You can approximate 9.8 ≈ 10.
How long from the time of launch does it take the bagel to reach its maximum altitude?
(a) 2s
(b) 3s
(c) 4s
(d) 6s
2
5. Continuation of the previous problem, same setup and launch velocity and angle θ0 .
What is the maximum altitude above street level obtained by the bagel?
(a) 45m
(b) 80m
(c) 90m
(d) 100m
6. Same setup, launch velocity, and angle θ0 .
How long does it take for the bagel to hit the ground?
(a) 5s
(b) 6s
(c) 7s
(d) 10s
7. Same setup, launch velocity, and angle θ0 .
What is the bagel’s speed when it hits the ground?
(a) 10 m/s
(c) 40 m/s
√
(c) 40 2 m/s
√
(d) 20 3 m/s
8 Same setup, launch velocity, and angle θ0 .
What is the angle θ0 that the bagel hits the ground, measured relative to the ground
(taking θ0 = 180◦ to be directed back toward the apartment.)
(a) 120◦ .
(b) 135◦ .
(c) 150◦ .
(d) 100◦ .
9. Same setup, launch velocity, and angle θ0 .
How far from the building does the bagel hit the street (i.e. what’s its range)?
(a) 210m
(b) 240m
(c) 280 m
(d) 300 m
10. Same setup, launch velocity, and angle θ0 .
3
Bruce has a countdown to launch time. At 5 seconds before launch time, Henrietta
starts from rest, directly below the window, and starts running at constant acceleration,
and manages to catch the bagel – touchdown!
Which of the following mostly closely approximates what her acceleration must be?
(a) 2m/s2
(b) 4m/s2
(c) 8m/s2
(d) 11m/s2 .
11 An airplane pilot flies in the +b
j direction (due North) relative to the ground (earth).
The plane moves with speed vP A = 100m/s relative to the air. The air moves with
velocity ~vAE = (50m/s)(bi + b
j) relative to the earth.
What is the plane’s velocity relative to the air?
√
(a) ~vP A = 50(−bi + 3b
j)m/s.
(b) ~vP A = 100b
jm/s.
(c) ~vP A = 50(bi + 3b
j)m/s.
(d) ~vP A = 50(bi + b
j)m/s.
12. What is the plane’s velocity relative to the ground?
(a) ~vP E = 150b
jm/s.
√
jm/s.
(b) ~vP E = 50(1 + 3)b
(c) ~vP E = 50(1 + 3)b
jm/s.
√
jm/s.
(d) ~vP E = 150 3b
4