Diagnostic test solutions for Physics 131

1. "milli" means divided by 1000 as in millimeter is a meter divided by 1000.  "pico" means divided by 1012.  If a molecule moves a picometer in a millisecond, what is its speed in m/s (express as a power of 10).Answer: v=10-12 m/10-3 s = 10-9 m/s
2. What is sin(45o) (use an elementary mathematical expression, not a calculator.) Answer 2-1/2 or 1/sqrt(2).  For sin(-45o), the answer is -2-1/2 or -1/sqrt(2).
3. Object A corresponds to the straight line, and object B to the curved line.

a. Which object is ahead at time 0? Answer object B
b. Which object has larger velocity at time 2.5 s? Answer object B
c. At what time (approximately) do the two objects have the same velocity? Answer t=2 s
d. What is the velocity of object A at t=4 s?  Answer: Object A always has velocity 4 m/s
 
4. Given that x + 3y = 20 and that 2x - y = 10, find x and y. Answer x=50/7, y=30/7
5. The clock says 10:00 o'clock.  The sun, shown schematically below, is directly overhead (but very far away.)  The hour hand (short hand) is 1.00 m long.  How long is the shadow of the hour hand on the level ground below?  Your answer should be a simple exact mathematical formula.  Answer: 1.0 m x cos(30o) or 31/2/2 m or sqrt(3)/2 m or (for half credit) 0.866 m (actually, give yourself full credit if you got this.)