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
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
2 answers
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?
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?
1 answer