Problema Solution
The velocity of a blood corpuscle in a vessel depends on how far the corpuscle is from the center of the vessel. Let R be the constant radius of the vessel; Vm, the constant maximum velocity of the corpuscle; r, the distance from the center to a particular blood corpuscle (variable); and Vr, the velocity of that corpuscle. The velocity Vr is related to the distance r accoding to the formula Vr-Vm(1-r^2/R^2). Find r when Vr-1/4Vm.
Answer provided by our tutors
You must mean:
Vr = Vm(1-r^2/R^2)
We need to find r when Vr = 1/4 Vm.
Plug Vr = 1/4 Vm into Vr = Vm(1-r^2/R^2):
1/4 Vm = Vm(1-r^2/R^2) divide both sides by Vm
1/4 = 1 - r^2/R^2
1 - r^2/R^2 = 1/4
r^2/R^2 = 1 - 1/4
r^2/R^2 = 3/4
r^2 = R^2(3/4)
r = √(R^2(3/4))