Asked by rem
Batman is surveying a cave, which is now known as the bat cave. He follows a passage 210.0m straight east, then 80.00m in a direction 60o west of north, then 150.0m at 45o west of south. After a fourth unmeasured displacement he finds himself back where he started. Find the magnitude and direction of the fourth displacement.
Answers
Answered by
mathhelper
translating all directions to standard trig notation, and using vectors:
210(cos0, sin0) + 80(cos150, sin150) + 150(cos225,sin225) + a(cosθ, sinθ) = (0,0
(210,0) + (-69.282, 40) + (-106.066, -106.066) + a(cosθ,sinθ) = 0
a(cosθ,sinθ) = (-34.652, 66.066)
a(cosθ,sinθ) = 74.602(cos117.677, sin117.677)
form a valid statement from my conclusion
210(cos0, sin0) + 80(cos150, sin150) + 150(cos225,sin225) + a(cosθ, sinθ) = (0,0
(210,0) + (-69.282, 40) + (-106.066, -106.066) + a(cosθ,sinθ) = 0
a(cosθ,sinθ) = (-34.652, 66.066)
a(cosθ,sinθ) = 74.602(cos117.677, sin117.677)
form a valid statement from my conclusion