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Vector Test

BLA Physics - Mr. Z.
Vector Test, 10/28/04

1. Definitions (20 pts)

The following questions deal with basics of vector math. Each question is worth 5 points.
  1. What is a vector?

  2. Label each of the following quantities as either "V" ("vector") or S ("scalar"), depending on whether or not that quantity needs a direction or is just a number:

    a) My displacement when traveling from home to school.

    b) The speedometer reading on a car.

    c) The initial velocity of a projectile.

    d) The difference in time between two runners.

    e) The mass of a bowling ball.

  3. Which picture shows the correct procedure for adding two vectors?

  4. Which of these problems is not an appropriate situation to solve with vector addition?

    a) I make two displacements in the course of a shopping trip and want to know my final displacement.

    b) A river is pulling me downstream at a speed of 3 m / s as I swim toward the opposite shore at a speed of 5 m / s.

    c) Two classmates have different displacements; I want to know who went the furthest.

    d) I know the displacement vector of each stroke in a Vector Minigolf hole, and want to know the displacement to the hole.

2. Using Vectors (30 pts)

In each of the following problems, use the motion equations we have from linear motion to answer the question, remembering that now those equations require you to do vector addition and scalar multiplication. You may use either graphical or numerical calculations.
  1. A dog moves at a velocity of (4x - 2y)(m / s).

    a) What is its displacement in 3 s?

    b) What is the displacement to where it was 1 s ago?

    c) If it started out at a position of (2m, 2m), what will its position be after 3 s?

  2. A person walking with an initial velocity of (-3x - 5y)(m / s) accelerates at a rate of (2x + 3y)(m / s²) for 5 s.

    a) What is his velocity at the end of that time?

    b) What is his displacement at the end of that time?

    c) What is his speed (the size of his velocity) at the start?

  3. A rabbit makes a displacement of (4x + 5y)m away from his hole to investigate a tantalizing smell. Now he wants to figure out which of three vectors will bring him back closest to his hole. For each of the three other vectors shown, find the total displacement if this vector is added to his original displacement, and find the distance from his hole.


3. Projectile Motion (30 pts)

  1. A juggling trick requires two people to pass balls back and forth while keeping up the rhythm of their juggling. When I make a short toss from one of my hands to the other, I throw the ball so that it rises up as high as my head. When I throw to the other person, if I want the toss to take the same amount of time to complete, should I aim to make it rise up just as high, higher, or not quite as high? Explain why, in a way that would make sense to someone who hasn't yet studied projectile motion.

  2. You drop a ball from the roof of a building, and discover that it takes 3 s for it to hit the ground. Then, you kick a soccer ball straight horizontally off of the roof. It hits the ground 120 m away. What initial velocity did you kick it with?

  3. A catapault fires a boulder with an initial velocity of (45x + 22y)(m / s).

    a) How long will it take the boulder to reach the wall of a castle, 180 m away?

    b) What will the velocity vector of the boulder be after that time?

    c) What will its displacement vector be after that time?

    d) The wall is 10 m high. Does the boulder hit the wall, fall short, or go over it?

    e) A speed of 50 m / s is required to break the wall. Is the boulder going fast enough?

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