Question

8. Two motorcycles, travelling at the same speed, approach an intersection, one from the north and the other from the west.
When one motorcycle is 110 m north and
the other is 80 m west of the intersection,
the distance between them is decreasing
at 30 m/s. Determine the speed of the motorcycles

Answer 1

n^2 + w^2 = d^2 ... d = √(n^2 + w^2)

differentiating ... 2 n dn/dt + 2 w dw/dt = 2 d dd/dt

dn/dt = dw/dt = s

2 * 110 * s + 2 * 80 * s = 2 * √(110^2 + 80^2) * -30


s is negative because the motorcycles are approaching the intersection

Answer 2

the distance z is
z^2 = x^2 + y^2
z dz/dt = x dx/dt + y dy/dt
since they have the same speed s, that means
z dz/dt = s(x+y)
at (80,110), that gives
10√185 (-30) = 190s
now finish it off
what does it means that s is negative?