1. Two birds are flying directly towards each other at the same speed If the first bird is flying at a velocity v, what is the the velocity of the second bird?

2. A United Airlines jet is flying at 300 km/hr, while an Air France Concord is speeding along at 1200 km/hr Both airplanes are flying at the same altitude If each aircraft experiences problems with an unruly passenger, and they both decide simultaneously to push the passenger out the door, which of the unruly passengers will hit the earth first? (Ignore air resistance)

3. Assuming the airplanes in the previous problem continue to travel at the same velocity after ejecting their respective passengers, where will the passengers land with respect to their aircraft's path?

4. The velocity function is all of the following EXCEPT

5. A police officer living on a planet with no air resistance drops a pair of handcuffs and a handkerchief from the same height at the same time Which one will reach the ground first?

6. What kind of function is an acceleration function describing one-dimensional motion?

7. In general, the acceleration of objects due to the earth's gravitational pull is

8. Kinematics is concerned with

9. A raindrop on a drizzly day takes one minute from the time it leaves the cloud until it hits your umbrella, 3 miles below The average velocity of the raindrop on its journey is

10. The average velocity and the instantaneous velocity of an object will be the same if

11. A car traveling at constant velocity v suddenly brakes in an effort to keep from hitting a rabbit which is 8 ft away If the braking action causes a constant deceleration a, how long does it take for the car to come to a complete stop?

12. In the previous question, how far did the car travel as it was braking?

13. If the car from the last two questions had initially been traveling at a speed of 10 ft/s, and experienced (from the braking) a deceleration of 5 ft/s2, would it have hit the rabbit which was 8 ft away? (Assume the rabbit was dazed and didn't move at all)

14. Find the derivative of 2x5 + x3 + + 5

15. Evaluate the derivative of x3 + x2 + 5x at x = - 2

16. Find the velocity of an object described by the position function x(t) = 3x2 + at time t = - 1

17. Find the acceleration of an object described by the position function x(t) = 3x2 + at time t = - 1

  • x(t) = (0, 0, - g)t2 + (2, 3, 4)t + (5, 0, 1)

18. What is the magnitude of the initial (ie at t = 0) velocity vector?

19. What is the position of the object at time t = - 2?

20. The object is moving

21. What is the acceleration of this object at time t = 25?

22. This equation might describe an object

23. In creature-land, the measure of one's hardcoreness is directly correlated to how high one can jump Unfortunately, creatures cannot jump straight up, but must take a running start If creature A jumps with initial velocity vector (2, 2, 5), and creature B jumps with initial velocity vector (5, 4, 2) (where the z-direction points upwards), which creature is more hardcore?

24. According to the previous question, which creature travels furthest during its jump?

25. Which function could describe the velocity of a ball being thrown horizontally off a fire escape?

26. Phin and Wittgenstein are hanging out on the moon when they decide to have a contest to see who can shoot a bullet farther Both use identical guns Phin decides to shoot at a 60 degree angle, while Wittgenstein holds his gun at 45 degrees when shooting Whose bullet lands the furthest away?

27. The office of the Harvard Review of Philosophy is located approximately 10 ft below the earth's surface The acceleration due to gravity experienced by members working in this office is

28. A couple of students at Putney decide to go bicycle riding one day Simon rides at a speed of 10 miles per hour, while Liz's average speed is 20 miles per hour After bicycling for several hours, both Simon and Liz come home and park their bicycles exactly where they started Simons's average velocity for the entire ride is

29. If, during their bike ride, Simon and Liz were always biking at a constant speed,

30. While sitting at his office desk, Stephen Greenblatt enjoys throwing crumpled pieces of paper into a wastebasket across the room Over the years, he has carefully kept track of all the different combinations of initial speeds and angles at which he can throw the crumpled pieces of paper while still making the same basket He hopes to some day have a complete list of all the possibilities Professor Greenblatt's efforts are useless because

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