Simple Nature - Light and Matter

G New York and Rome are at about the same latitude, so the earth’srotation carries them both around nearly the same circle. Do the two citieshave 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 underthe influence of gravity. Sketch the car’s velocity vectors and accelerationvectors. Pick an interesting point in the motion and sketch a set of forcevectors acting on the car whose vector sum could have resulted in theright acceleration vector.IThe following is a question commonly asked by students:“Why does the force vector always have to point in the same directionas the acceleration vector? What if you suddenly decide to change yourforce on an object, so that your force is no longer pointing in the samedirection that the object is accelerating?”What misunderstanding is demonstrated by this question? Suppose, forexample, a spacecraft is blasting its rear main engines while moving forward,then suddenly begins firing its sideways maneuvering rocket aswell. What does the student think Newton’s laws are predicting?J Debug the following incorrect solutions to this vector addition problem.Problem: Freddi Fish TM swims 5.0 km northeast, and then 12.0 km in thedirection 55 degrees west of south. How far does she end up from herstarting point, and in what direction is she from her starting point?Incorrect solution #1:5.0 km+12.0 km=17.0 kmIncorrect solution #2:√(5.0 km)2 + (12.0 km) 2 =13.0 kmx / Discussion question H.Incorrect solution #3:Let A and B be her two ∆r vectors, and let C = A + B. ThenA x = (5.0 km) cos 45 ◦ = 3.5 kmB x = (12.0 km) cos 55 ◦ = 6.9 kmA y = (5.0 km) sin 45 ◦ = 3.5 kmB y = (12.0 km) sin 55 ◦ = 9.8 kmC x = A x + B x= 10.4 kmC y = A y + B y= 13.3 km√|C| = Cx 2 + Cy2= 16.9 kmdirection = tan −1 (13.3/10.4)= 52 ◦ north of eastSection 3.4 Motion In Three Dimensions 207