Answer :
The change in distance between the two after 15 minutes is 2.124 mi/h.
What is Velocity?
Velocity is defined as the rate of change in displacement (distance) with time. It's a vector quantity so it has both magnitude and direction. Velocity is given by the formula:
Velocity = Distance / Time
If one walks east at 3 mi/h and the other walks northeast at 2 mi/h, then after 15 minutes, their distance will be:
Distance = Velocity × Time
Distance₁ = 3 mi/h (15 mins)(1 hour/60 mins)
Distance₁ = 0.75 mile east
Distance₁ = 2 mi/h (15 mins)(1 hour/60 mins)
Distance₁ = 0.5 mile northeast
Using trigonometric function and Pythagorean theorem, we can determine the distance between the two people.
d² = (0.5 sin 45°)² + (0.5 cos 45° - 0.75)²
d² = 0.282
d = 0.531 mi
So, After 15 mins, the distance will be 0.531 mi and the change in distance in mi/h is:
(0.531 mi / 15 mins)(60 mins / hour) = 2.124 mi/h
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