A boy starts walking north at a speed of 1.5 m/s, and a girl starts walking west at the same point P at the same time at a speed of 2 m/s.

Question

A boy starts walking north at a speed of 1.5 m/s, and a girl starts walking west at the same

point P at the same time at a speed of 2 m/s. At what rate is the distance between the boy and the girl

increasing 6 seconds later ?

Answer 1

The distances are shown as a function of time. So the distance they are apart as a function of time is:

d₃ = √(d₁² + d₂²)

d₃ = √((1.5t)² + (2t)²)

d₃ = √(2.25t² + 4t²)

d₃ = √(6.25t²)

d₃ = 2.5t

To find the rate, take the derivative

d₃/dt = 2.5 m/s

The easier approach is just to consider the rates as vectors then you just take the square root of the sum of the squares of the velocities.