Magnitude and direction

John drives 16 km directly west from Orion to Chester at a speed of 98 km/h, then directly south for 8.0 km to Seiling at a speed of 85 km/h, then finally 34 km southeast to Oakwood at a speed of 107 km/h.

(a) What was the change in velocity during this trip?
magnitude______ km/h ?
direction______ south of east ?

(b) What was the average acceleration during this trip?
magnitude________ km/h^2 ?
direction________ south of east ?

Let direct 0 be due East and positive angles be measured South of East.

(a)
Vi = 98 @ 180 deg
Vf = 107 @ 45 deg

DeltaV = Vf - Vi

Decompose into (x, y)
Vi = (98 * cos(180), 98 * sin(180))
Vf =(107 * cos(45), 107 * sin(45))
DeltaV = (107 * cos(45) - 98 * cos(180), 107 * sin(45) - 98 * sin(180))
DeltaV = (107 * sqrt(2)/2 - 98 * -1, 107 * sqrt(2)/2 - 98 * 0)
DeltaV = (107 * sqrt(2)/2 + 98, 107 * sqrt(2)/2)
DeltaV = ((107 * sqrt(2) + 196) / 2, 107 * sqrt(2)/2) = (Dx, Dy)

Magnitude = sqrt(Dx^2 + Dy^2)
Direction = arctan(Dy / Dx)

(b) a = DeltaV / t
t = d1 / r1 + d2 / r2 + d3 / r3
t = 16 / 98 + 8 / 85 + 34 / 107

Magnitude = Magnitude from part (a) / t from above
Direction is the same as part (a)