Vector Solutions non 90

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Vector Solutions non 90

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  1. Vector Solutions

    Slide 1 - Vector Solutions

    • With no right angles
  2. A plane cruises a 425 km/hr on a heading of 50.0o, while encountering a wind blowing towards 325o at 135 km/hr.  What is the plane’s velocity over ground?

    Slide 2 - A plane cruises a 425 km/hr on a heading of 50.0o, while encountering a wind blowing towards 325o at 135 km/hr. What is the plane’s velocity over ground?

  3. A plane cruises a 425 km/hr on a heading of 50.0o,

    Slide 3 - A plane cruises a 425 km/hr on a heading of 50.0o,

    • while encountering a wind blowing towards 325o at 135 km/hr.
    • What is the plane’s velocity over ground?
  4. Component Method

    Slide 4 - Component Method

    • Break each vector into X and Y components
    • Add the X’s and add the Y’s
    • Combine the Total X and Total Y into a Resultant
  5. A plane cruises a 425 km/hr on a heading of 50.0o,

    Slide 5 - A plane cruises a 425 km/hr on a heading of 50.0o,

    • 50o
    • Y
    • X
    • 425 km/hr
  6. A plane cruises a 425 km/hr on a heading of 50.0o,

    Slide 6 - A plane cruises a 425 km/hr on a heading of 50.0o,

    • 50o
    • Y = (425km/hr)(cos50o)
    • = 273 km/hr
    • X = (425km/hr)(sin50o)
    • = 326 km/hr
    • 425 km/hr
    • X
    • Y
    • Y
    • X
  7. while encountering a wind blowing towards 325o at 135 km/hr.

    Slide 7 - while encountering a wind blowing towards 325o at 135 km/hr.

  8. while encountering a wind blowing towards 325o at 135 km/hr.

    Slide 8 - while encountering a wind blowing towards 325o at 135 km/hr.

    • Y
    • X
    • 135 km/hr
    • 35o
  9. while encountering a wind blowing towards 325o at 135 km/hr.

    Slide 9 - while encountering a wind blowing towards 325o at 135 km/hr.

    • Y = (135km/hr)(cos35o)
    • = 111 km/hr
    • X= (135km/hr)(sin35o)
    • = 77.4 km/hr
    • 135 km/hr
    • 35o
  10. Combine the Y-components

    Slide 10 - Combine the Y-components

    • Y = 111 km/hr
    • Y = 273 km/hr
    • Ytotal = 384 km/hr
  11. X= -77.4 km/hr

    Slide 11 - X= -77.4 km/hr

    • Combine the X-components
    • X = 326 km/hr
    • Xtotal = 249 km/hr
  12. Find the Resultant

    Slide 12 - Find the Resultant

    • Xtotal = 249 km/hr
    • Ytotal = 384 km/hr
  13. Find the Resultant

    Slide 13 - Find the Resultant

    • C2 = A2 + B2
    • C =  (384 km/hr)2 + (249 km/hr )2
    • C= 458 km/hr
    • = tan-1 opp
    • adj
    • = tan-1 249 km/hr 384 km/hr
    • = 33.0o
    • A = 384 km/hr
    • B = 249 km/hr
    • B
    • A
    • C
    • Answer: 458 km/hr @ 33.0o
  14. Use the Law of Cosines and the Law of Sines to solve the parallelogram

    Slide 14 - Use the Law of Cosines and the Law of Sines to solve the parallelogram

  15. A plane cruises a 425 km/hr on a heading of 50.0o,

    Slide 15 - A plane cruises a 425 km/hr on a heading of 50.0o,

    • while encountering a wind blowing towards 325o at 135 km/hr.
    • What is the plane’s velocity over ground?
    • 50.0o
    • 325o
    • 85o
    • 425 km/hr
    • 135 km/hr
  16. Complete the parallelogram

    Slide 16 - Complete the parallelogram

    • 85o
    • 85o
    • 95o
    • 95o
  17. Law of Cosines

    Slide 17 - Law of Cosines

    • 95o
    • b
    • a
    • c
    • c =  a2 + b2 - 2abcosC
  18. Slide 18

    • 95o
    • b = 425 km/hr
    • a = 135 km/hr
    • c
    • c =  a2 + b2 - 2ab cosC
    • c =  (135 km/hr)2 + (425 km/hr)2 - 2(135 km/hr)(425 km/hr) cos(95o)
    • c = 457 km/hr
  19. Law of Sines

    Slide 19 - Law of Sines

    • sin B = sin C
    • b c
    • B = sin-1 (425 km/hr) sin (95o)
    • (457 km/hr)
    • B = 67.9o
    • 95o
    • b = 425 km/hr
    • a = 135 km/hr
    • B
    • C = 457 km/hr
  20. c

    Slide 20 - c

    • Direction of Resultant = 325o + 67.9o = 393o
    • Since North is 360o, the Resultant is pointing at 33o
    • B
    • 325o
    • 33o
  21. 457 km/hr

    Slide 21 - 457 km/hr

    • A plane cruises a 425 km/hr on a heading of 50.0o,
    • while encountering a wind blowing towards 325o at 135 km/hr.
    • What is the plane’s velocity over ground?
    • Answer: 457 km/hr @ 33o
    • 33o