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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 20, find are the x and y components.

16) If a tree casts an 12.00 m shadow when the sun is at 65 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.