z/Discussion question H.G New York and Rome are at about the same latitude, so the earth’s
rotation carries them both around nearly the same circle. Do the two cities
have the same velocity vector (relative to the center of the earth)? If not,
is there any way for two cities to have the same velocity vector?
H The figure shows a roller coaster car rolling down and then up under
the influence of gravity. Sketch the car’s velocity vectors and acceleration
vectors. Pick an interesting point in the motion and sketch a set of force
vectors acting on the car whose vector sum could have resulted in the
right acceleration vector.
I The following is a question commonly asked by students:
“Why does the force vector always have to point in the same direction
as the acceleration vector? What if you suddenly decide to change your
force on an object, so that your force is no longer pointing in the same
direction that the object is accelerating?”
What misunderstanding is demonstrated by this question? Suppose, for
example, a spacecraft is blasting its rear main engines while moving for-
ward, then suddenly begins firing its sideways maneuvering rocket as
well. What does the student think Newton’s laws are predicting?
J Debug the followingincorrectsolutions to this vector addition prob-
lem.
Problem: Freddi FishTMswims 5.0 km northeast, and then 12.0 km in the
direction 55 degrees west of south. How far does she end up from her
starting point, and in what direction is she from her starting point?
Incorrect solution #1:
5.0 km+12.0 km=17.0 km
Incorrect solution #2:√
(5.0 km)^2 + (12.0 km)^2 =13.0 km
Incorrect solution #3:
LetAandBbe her two∆rvectors, and letC=A+B. Then
Ax= (5.0 km) cos 45◦= 3.5 km
Bx= (12.0 km) cos 55◦= 6.9 km
Ay= (5.0 km) sin 45◦= 3.5 km
By= (12.0 km) sin 55◦= 9.8 km
Cx=Ax+Bx
= 10.4 km
Cy=Ay+By
= 13.3 km
|C|=√
C^2 x+Cy^2
= 16.9 km
direction = tan−^1 (13.3/10.4)
= 52◦north of eastSection 3.4 Motion in three dimensions 211