Peggy drives from Cornwall to Atkins Glen in 52 min. Cornwall is 75 km from Illium in a direction 26° west of south. Atkins Glen is 27.1 km from Illium in a direction 16° south of west. Use Illium as your origin.
(a) Draw the initial and final position vectors. (Do this on paper. Your instructor may ask you to turn in this work.)
(b) Find the displacement during the trip.
magnitude km
direction ° north of east
(c) Find Peggy's average velocity for the trip.
magnitude km/h
direction ° north of east
Could someone help me solve this please I tried but i got it wrong...
I got 64.82 km and 14.57 degrees for part b and 74.79 km and 14.57 degree for part c, but they where wrong; I don't understand why?
Thank you, and sorry for reposting.
We have triangle with two known sides, a =27.1 km and b =75 km, and the angle α between them
α = 90 º - 16 º -26 º = 48º.
Let’s use the law of cosines to solve for the third side (magnitude of displacement)
r = sqrt(a² +b²-2•a•b•cosα) = sqrt(75² +27.1² - 2•75•27.1•cos48º) = 60.34 km.
Then use the law of sines to find the angles opposite to side a = 27.1 km.
a/sinθ = r/sinα .
sin θ = sinα •a/r =sin48•27.1/60.34 = 0.333.
θ = 19.6º,
φ = 90 º – (26 º -19.5 º) = 90 º – 6.5 º = 83.5 º (N of E)
v(average) = r/t = 60.34•60/52 = 69.62 km/hr
Its direction will be the same as the direction of displacement.