Vectors- Motion in Two Dimensions

1
Vectors- Motion in Two Dimensions

• Magnitude the amount or size of something
• Scalar a measurement that involves
• magnitude only, not direction
• EX mass, time, temperature, distance,
• speed (can never be negative)
• Vector has both magnitude and direction
• EX displacement, velocity, acceleration
• (can be negative due to direction)

2

• Vectors can be added and subtracted.
• If two vectors point in the same direction, they
  will add together to form a larger vector.
  (Largest sum)
• If two vectors point in opposite directions,
  they subtract, with the bigger vector indicating
  the direction of the result. (Smallest sum)
• EX Vectors 6m and 5m. Same direction, sum is
  11m. Opposite directions, 1m.

3

• Resultant the final vector that represents
• the combination of a series of
• vectors.
• Components the x and y vectors that add
• together to form the resultant.
• EX Vector length 10, at 300, find the
• x and y components. (draw a right triangle)

4

• Trig functions- sine, cosine, tangent are useful
  to resolve the vectors into components, and to
  solve for missing angle. (Use only with right
  triangles)
• SOH- CAH- TOA
• Sine the ratio of the side opposite the angle,
  and the hypotenuse.
• (Sine q Opposite/Hypotenuse)
• Cosine the ratio of the side adjacent the
• angle, and the hypotenuse.
• (Cosine q Adjacent/ Hypotenuse)

5

• Tangent the ratio of the side opposite the
• angle to the side adjacent to the
• angle. (Useful in finding missing
• angle measures)
• (Tangent q Opposite / Adjacent)
• Example 1 Find the x and y components of a
  velocity that is 25 m/s at 400 to the horizontal)
• Example 2 A hill is 80m long, and 15m high.
  What is the angle of the slope?