amy is traveling at 60 mph on the highway, due north. The on-ramp nearby starts

Question

amy is traveling at 60 mph on the highway, due north. The on-ramp nearby starts out going west, and then curves around so that eventually it is also north, parallel to the highway. Bob appears, traveling 40 mph going west. what is his speed relative to Amy? In the next moment, he is heading due Northwest, now going 50 mph. what is his speed relative to Amy at this point? Later on, he is finally on the northward portion of the ramp, and has accelerated up tp 55mph. What now is his speed Relative to Amy?

Explanation / Answer

let north-south be y axis and east west be x axis

so

1) amy velocity = 60 j

bob velocity = -40i

rel velocity of bob w.r.t. amy = -40i - 60j

magnitude = 72.11

direction = 56degree north of west

2)

amy velocity = 60 j

bob velocity = -50cos45i + 50cos 45j = -35.35i + 35.35 j

rel velocity of bob w.r.t. amy = -35.35i + 34.65 j

magnitude = 49.5 mph

direction = taninverse(34.65/35.35) = 44.42 north of west

3)

amy velocity = 60 j

bob velocity = 55j

rel velocity of bob w.r.t. amy = -5 j

magnitude = -5 mph

direction = due north

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