IYJ  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.

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Presentation transcript:

IYJ  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/s5m/s 15 m/s

Similarly orientated vectors can be subtracted in the same manner. - = 10m/s5m/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 1 Join vector tails at a common origin. A B

Step 2 Construct a parallelogram. A B

Step 3 The 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 boat 12 m/s

Step 2 current 5 m/s boat 12 m/s

Step 3 current 5 m/s boat 12 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 Strong 1,250 N Stuck in the mud Oxie

Celebratory Random Clip Art Good Job!!