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Math Review

Math Review. S o/h C a /h T o/a Sine = opposite/ hypotenuse Cosine = adjacent/ hypotenuse Tangent = opposite/ adjacent. Find x 3 45° x 5 4

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Math Review

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  1. Math Review • So/h Ca/h To/a • Sine = opposite/ hypotenuse • Cosine = adjacent/ hypotenuse • Tangent = opposite/ adjacent

  2. Find x 3 45° x 5 4 10 30° x

  3. Pythagorean Theorem • a2 + b2 = c2 10 8 6 4 3 6

  4. Chapter 3 2 Dimensional Motion

  5. Vectors vs. Scalars • Scalar: A quantity that has magnitude and no direction. • Speed. Volume. Height. • Vector: A quantity that has magnitude and Direction. • Velocity. Force. Displacement.

  6. Vectors • Vectors are represented by “vector arrows”, the length of the arrow represents the magnitude and the direction is that of the vector. 2.5m/s East 1m/s North

  7. Adding and Subtracting Scalars • 2Gallons + 3Gallons = ? • 5Gallons • 25Feet – 12.5Feet = ? • 12.5Feet

  8. Protractor Worksheet

  9. Adding and Subtracting Vectors • Must have the same units! • Resultant: A vector that represents the sum of two or more Vectors. • Vectors can be added Graphically and Mathematically.

  10. Adding Vectors Graphically • When adding two vectors draw the Vectors in the x direction first. • After drawing a Vector the next Vector must be drawn from the tip of the one before it so that its tail is touching it. • (TIP TO TAIL) • Draw a Line from the start to the finish, that is your resultant, Measure it and find the direction using a protractor.

  11. Add the Vectors Graphically • 2m East, 2m East, 3m North • Remember Magnitude and Direction.

  12. Adding Vectors Algebraically • 1. Find x and y components of all vectors • 2. Place components into the appropriate column • 3. Add each column • 4. Subtract North – South / East – West • 5. Draw x Resultant then Tip to Tail y Resultant • 6. Find the magnitude of the resultant • 7. Find the direction of the resultant.

  13. Question • Following directions on a map, a pirate walks 45.0m north then turns and walks 7.5m east. What is his total displacement?

  14. Components

  15. Components of a Vectors • Question: A Plane travels 45 degrees South of West for 600miles. How far South must another plane travel, then how far West must the Plane travel to end up in the same place?

  16. Components + Vector Addition • A football player runs directly down field for 35m before turning to the right at an angle of 25 degrees from his original direction and running an additional 15m before getting tackled. What is the magnitude and direction of the runner’s total displacement?

  17. Home Work • Page 109 • #’s 21 (a. 5 blocks 53degrees NoE, b. 13 blocks), 24 ( 108M, -19.1m), • 26( 240m at 57.2 degrees SoW)

  18. Projectile Motion • The curved path that an object follows when thrown, launched, or otherwise projected near the surface of the Earth. • The path of an object that is in two dimensions under the influence of gravity.

  19. Projectile Motion

  20. Projectile Equation(s)

  21. Non Horizontal Projectile Motion

  22. Questions • A stunt man jumps from the top of one building to the top of another building 4.0m away. After a running start, he leaps at a velocity of 5.0m/s at an angle of 15 degrees with respect to the flat roof. Will he make it to the other roof, which is 2.5m lower than the building he jumps from?

  23. A golfer hits a golf ball at an angle of 25 degrees to the ground. If the golf ball covers a horizontal distance of 301.5m, what is the ball’s maximum height?

  24. A baseball is thrown at an angle of 25 degrees relative to the ground at a speed of 23m/s. If the ball was caught 42.0m from the thrower, how long was it in the air?

  25. Salmon jump waterfalls to reach their breeding grounds. One Salmon starts 2.00m from a waterfall that is 0.55m tall and jumps at an angle of 32 degrees. What must the salmons minimum speed be to reach the waterfall?

  26. Relative Velocity The motion of an object relative to another objects frame of reference. Example: A boat travels straight across a river at 5m/s East, but the rivers current is 1m/s South. What is the Relative Velocity of the boat? Answer 5.1m/s 11.3 degrees South of East

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