Two free vortices of equal strength, but opposite direction of rotation, are superimposed with a uniform flow (v~ = uˆi). the first vortex, of clock-wise rotation, is located at (0,h) and the second is located at (0,-h). the stream function for a vortex of positive strength is given by

D.

Explanation:

In order to know how long after Bill released his rock should Ted throw his if they want the stones to hit the water simultanously, we need to calculate the time needed to hit the water to both rocks independent each other, and just take the difference.

For the rock dropped by Bill, as the only influence on it is gravity (accelerating it downwards with an acceleration equal to g), and v₀ =0, we can use the following kinematic equation:

where y = height = 40 ft.

As all the parameters are given in SI units, it is  advisable to convert this value to m, as follows:

Now, we can solve for t, as follows:

For the rock thrown down at 10 m/s, the kinematic equation we just have used becomes:

This leaves us a quadratic equation on t, as follows:

Taking the positive root, we have:

t = -1.02 s + 1.88 s = 0.86 s

So, in order to get that both rocks hit the water at the same time, Ted will need to wait the difference between both times:

Δt = 0.86 s - 1.58s = -0.72 s