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Regents Physics

Regents Physics. Vectors and Scalars What is a Vector? A scalar? A vector is a quantity that has both magnitude and direction A scalar has only magnitude For example: Distance vs. Displacement Speed vs. velocity. Drawing Vectors. A vector has magnitude and direction

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Regents Physics

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  1. Regents Physics • Vectors and Scalars • What is a Vector? A scalar? • A vector is a quantity that has both magnitude and direction • A scalar has only magnitude • For example: • Distance vs. Displacement • Speed vs. velocity

  2. Drawing Vectors • A vector has magnitude and direction • each vector is drawn to scale and includes a tip, indicating a direction N V = 100.0 m/s east Tip Tail E W The length is defined by creating a scale S Scale 1.0 cm = 10.0 m/s The coordinate axis system defines the direction of the vector

  3. Tip to Tail Triangle Method..How do we graphically add/subtract vectors Tail of V2 to tip of V1 Resultant Vector (R) = V1 + V2 V2 V1 The resultant vector is an equal expression of vectors V1 , V2

  4. Tip to Tail... V1 east N V2 north R Put on axis and use tip to tail method V2 north W E V1 east Measure the length of the resultant! S

  5. Vector addition example • A person walks 24.0 m north and 12.0 m east. Determine the position and magnitude of the resultant vector of this motion. • First, make a scale for the vectors • Draw a coordinate axis • Draw and the label the vectors • Draw and measure the resultant vector!

  6. Vector addition problem #2 • A plane flies at 200.0 miles per hour north when it encounters a crosswind of 80.0 miles per hour from the west. Determine the position and magnitude of the resultant vector of this motion.

  7. These are equal expressions…right?!

  8. Notice both vectors start at the same origin This method can also be used when we are not using tip to tail addition… and we also get the same results!

  9. Example • Find the resultant vector of the following two vectors We use dashed lines to represent the mirror images of the vectors

  10. Rotate green A vector 180 degrees and give it a negative sign! Just remember..tip to tail B A Our resultant vector is now B - A and has a different magnitude and direction!

  11. A car drives 100.0 km at an angle of 35 degrees north of east. Find the vectors d1 east and d2 north of this motion. What if we START with the resultant? V2 north 35 ° V1 east Just draw and measure the vectors!

  12. Practice Problem... • A package is dropped from a plane and is “off target” by 100ft to the west. If the distance to the ground is 500ft. • (a) What is the resultant vector of this motion? • (b) What is the angle from the negative y - axis of the resultant vector? end

  13. Vectors Relative Velocities The Boat and the Plane

  14. The Boat • If a motor boat were to head straight across a river, it would not reach the shore directly across from its starting point. • The river current influences the motion of the boat and carries it downstream. • The motor boat may be moving with a velocity of 4 m/s, but… • While the speedometer of the boat may read 4 m/s, its speed with respect to an observer on the shore will be greater than 4 m/s.

  15. The Plane • We can apply the same logic to a plane

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