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Date: ___________

Vector worksheet -
Honors Physics

1. Define a vector.

2. Describe how
vectors are represented:

a) on a graph.

b) algebraically

3) Which of the
following statements is not true regarding vectors?

a) The magnitude of a vector is described by a
scalar.

b) A scalar and a vector are opposite in
direction.

c) The direction of a vector may be expressed by
an angle.

d) A vector may be expressed by x and y components.

e) A vector must be described by a magnitude and
a direction.

4) What is the
difference between a vector and a ray?

5) Given a vector
connecting two the following two points in space find the magnitude of the
vector: from (1, 3) to (-2, 5).

6) Given a vector
connecting two the following two points in space find the direction of the
vector: from (1, 3) to (-2, 5).

7) Given a vector
connecting two the following two points in space find the opposite of the
vector: from (1, 3) to (-2, 5). Show your answer algebraically and
graphically.

8)
If two vectors **A** and **B** are parallel, vector **A** has a magnitude of 3 and vector **B** has a magnitude of 8, find all of the
possible magnitudes and directions of the resultant when taking sum and difference of **A** and **B.**

9) Vector **A** has a magnitude of 3.00 in the
positive y direction and vector **B** has
a magnitude of 7.00 in the positive x direction. What is the magnitude and direction of the
resultant vector **A**+**B**?

10) Vector **A** has a magnitude of 3.00 in the
positive y direction and vector **B** has
a magnitude of 7.00 in the positive x direction. What is the magnitude and direction of the
resultant vector **A**-**B**?

11) On a graph, what
represents the magnitude of a vector?

12) On a graph,
which transformations leave a vector unchanged; rotation, reflection,
translation or scaling?

13) Find **A**+**B**,
where and

a) Graphically

b) Algebraically

c) Find the magnitude and direction of **A**+**B**.

d) Find the components of **A**+**B**.

14) Find **A**-**B**,
where and

a) Graphically

b) Algebraically

c) Find the magnitude and direction of **A**+**B**.

d) Find the components of **A**+**B**.

15) Given a vector
of magnitude 7.00 at 20º, find are the x and y components.

16) If a tree casts
an 12.00 m shadow when the sun is at 65º with respect to horizontal, how tall
is the tree?

17) If a boat rows
0.40 miles across a river with still water at a speed of 7.00 mph, how far down
stream would the boat land if the river had a current of 9.00mph?

18) If an airplane
is flying at 300 mph parallel to a 80mph wind, which of the following speeds,
to an observer on the ground, find the fastest and the slowest that the airplane
be flying?

19) If an airplane
is flying at 300 mph due north on a still day, with 80mph westerly wind find the true speed of
the airplane.