Calc problem with changing river velocity y=3sin(Pi*x/40)

[munkhuu1]

Homework Statement

40mm wide blood vessel. and flow is fastest in the middle of the vessel which is 3mm/sec. Blood flow speed is f(x)=3sin(pix/40) where x is the distance from the wall. and tumor cell on one side is swept into to blood and movies 5mm/s directly across the vessel. the tumor cell travels in one plane.

Homework Equations

when will the tumor cell will travel it's fastest?
Where will the tumor cell land on the opposite side of the blood vessel compared to where it started?
What is the acceleration vector of the tumor cell just before it lands on the opposite side of the blood vessel?

The Attempt at a Solution

i think it will travel fastest in the middle of the vessel. i got square root of 34. I am not sure how to explain why though.

i tried to find where it will land but since the blood velocity is changing i didnt know what to do. Do i find the deriv of the blood speed equation?

accel is the deriv of speed so i think i would find deriv of the velocity then plug 40?

help please thank you.

 

[HallsofIvy]

You say the cell "moves 5mm/s directly across the vessel" so you can model the movement across as x= 5t in mm. For x from 0 to 20 mm, in the center of the blood vessel, which, of course, means t from 0 to 4 sec, y= 3sin(pix/40)t= 3sin(pix/40)(x/5).

After 4 seconds, x change to the distance to the other side so you will have x going from 20 to 0.

 

[munkhuu1]

but how would i use time to solve, there is no t value. can you go little deeper about how to do it? thank you.