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If you were running the 100 meter dash with a tail wind would you go faster or slower?

If you were running the 100 meter dash into a head wind would you go faster or slower?

If you were running the 100 meter dash with a wind blowing from the side would you go faster or slower?

Vectors

Conceptual Physics

What is a vector?

A vector is an arrow representing magnitude and direction.

The longer the arrow the __________ the magnitude.

The shorter the arrow the _________ the magnitude.

Addition of vectors:

Two or more vectors may be added together to produce their addition. If two vectors have the same direction, their resultant has a magnitude equal to the sum of their magnitudes and will also have the same direction.

+ =10m/s 5m/s

15 m/s

Similarly orientated vectors can be subtracted in the same manner.

- =10m/s 5m/s

Subtracting Vectors

5 m/s

Parallelogram method:

In the parallelogram method for vector addition, the vectors are translated, (i.e., moved) to a common origin and the parallelogram constructed as follows:

A

B

Step 1Join vector tails at a common origin.

A

B

Step 2

Construct a parallelogram.

A

B

Step 3The resultant is the diagonal of the parallelogram drawn from the common origin.

A

B

Sample #1

A plane is flying due north at 80 m/s. It encounters a wind that is directed due east, with a magnitude of 40 m/s. What is the resultant speed of the plane?

Use a scale of 1 cm = 10 m/s.

The sketch below shows the general orientation of the vectors, but is not drawn to scale.

plane (80 m/s) wind (40m/s)

Step 1

plane(80 m/s)

wind

(40m/s)

Step 2

wind

(40m/s)

plane(80 m/s)

Step 3

wind

(40m/s)

plane(80 m/s)

Measure your resultant length then multiply by the scale to find the resultant speed.

Sample #2

A boat travels due south on a river at a speed of 12 m/s. It encounters a current of 5 m/s that is directed 35 degrees south of east. What are the new direction and speed of the boat?

Use a scale of 1 cm = 2m/s

The sketch below shows the general orientation of the vectors, but is not drawn to scale.

boat (12 m/s) current (5 m/s)

Step 1

current 5 m/s

boat12 m/s

Step 2

current 5 m/s

boat12 m/s

Step 3

current 5 m/s

boat12 m/s

Sample #3

A tractor is stuck in the mud. In order to free the tractor Farmer Susie uses 2 oxen to pull it out. The oxen pull on two ropes separated by an angle of 60°. Each pulls with a force of 700 N. What is the combined pulling force of the 2 oxen.

A Helpful Diagram

60°

700 N

700 N

Strong

1,250 N

Stuck in the mud

Oxie

Celebratory Random Clip ArtGood Job!!