Position vectors of two sprinters running on a flat field relative to a fixed point o at time t are given by..

Question

ra(t) = (5t - 1)i + (1 - t)j
rb(t) = 4ti + (t^2 - t)j

Question: Obtain an expression for the magnitude of the distance between between the sprinters.
Thanks

Answer 1

Let
d(t) = distance between runners at time t

d(t) = √{[(5t - 1) - 4t]² + [(1 - t) - (t² - t)]²}
d(t) = √{(t - 1)² + (1 - t²)²}
d(t) = √{t² - 2t + 1 + 1 - 2t² + t^4}
d(t) = √(t^4 - t² - 2t + 2)