2 Dimensional Motion-Kinematics

QS 1: An airplane wishes to travel 800 km northeast of a starting point. There is a wind blow towards the east at 100km/h. Assuming the maximum speed of the plane in still air is 500km/h,

a: what course should the pilot steer to arrive in minimum time?

b: How long does the trip take?

2 answers

n = speed north

n - 100 = speed east

n^2 + (n - 100)^2 = 500^2

2 n^2 - 200n + 10000 - 250000 = 0

n^2 - 100 n - 120000 = 0

solve for n

the north distance is 400√2

time = distance / speed

the bearing (Θ , east of north)
... tan(Θ) = (n - 100) / n
a. Vp + 100 = 500[45o].
Vp + 100 = 500*sin45 + i500*Cos45,
Vp + 100 = 353.6 + 353.6i,
Vp = 253.6 + 353.6i = 435km/h[35.6o]E. of N.
Tan A = X/Y.

b. d = V*T.
800 = 435 * T,

=
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