i really your need help,i don't understand the problem. 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 by the equation Vr=Vm (1-r^2 /R^2). Find r when Vr=1/4Vm.
just plug it in:
1/4 Vm = Vm(1-r^2/R^2)
1 = 4 - 4r^2/R^2
4r^2/R^2 = 3
r^2 = 3/4R^2
r = √3/2 R
To find the value of r when Vr = 1/4Vm, we can substitute Vr = 1/4Vm into the equation Vr = Vm(1 - r^2/R^2). This will allow us to solve for r.
Substituting Vr = 1/4Vm into the equation, we get:
1/4Vm = Vm(1 - r^2/R^2)
Now, let's solve for r.
First, let's simplify the equation by canceling out Vm on both sides:
1/4 = 1 - r^2/R^2
Next, let's isolate the term with r by subtracting 1 from both sides of the equation:
1/4 - 1 = - r^2/R^2
To simplify further, let's combine the fractions:
-3/4 = - r^2/R^2
Now, let's multiply both sides of the equation by -1:
3/4 = r^2/R^2
To eliminate the fraction on the right side, let's multiply both sides by R^2:
3/4 * R^2 = r^2
Now, take the square root of both sides to solve for r:
√(3/4 * R^2) = r
Finally, simplifying the square root and rearranging, we get the value of r:
r = (√3/2)R
So, when Vr = 1/4Vm, the value of r is (√3/2)R.