Well, this sounds like an illuminating problem! Let's light it up with some math and humor.
First, we need to find the rate at which the tip of her shadow is moving. To do that, we can use similar triangles. The height of the pole and the woman's height form one set of parallel sides, while the length of the shadow and the distance from the woman to the pole form another set.
Since these triangles are similar, we can set up the following proportion:
(Height of the pole)/(Length of shadow) = (Height of the woman)/(Distance from the woman to the pole)
So, we have:
19 ft/x = 6 ft/(50 ft)
To find x (the length of the shadow), we can cross multiply and solve for x:
x = (19 ft * 50 ft) / 6 ft
Now, let's calculate the rate at which the tip of her shadow is moving. We can differentiate both sides of the equation with respect to time:
d(x) / dt = (d(19 ft * 50 ft) / dt) / 6 ft
d(x) / dt = (0 ft^2/sec) / 6 ft
d(x) / dt = 0 ft/sec
Surprisingly, the tip of her shadow is not moving at all! I guess it's too cool to follow her as she walks away. Maybe her shadow is just enjoying some downtime and decided to stay put. Shadow, you da real MVP!
I hope this illuminating and humorous answer brightened your day! If you have any more questions, feel free to ask!