Question

After eight years of dating, a female broke up with her lover on a rainy day. They chose to split up in the same area where everything about them began. The boy is crying and rushing north at a speed of 5 feet per second, while the girl is strolling east at a speed of 1 foot per second, wondering if she made the right decision. 5 seconds after they started traveling to a new life without each other, how quickly are they detaching from each other?

Answer 1

Distance traveled by the boy is $5t$ feet. Distance traveled by the girl is $1t$ feet.

By the Pythagorean Theorem distance $s$ between them is

$$s(t)=\sqrt{(5t)^2+(1t)^2}=\sqrt{26}t(ft)$$

How quickly are they detaching from each other

$$v(t)=s'(t)=(\sqrt{26}t)'=\sqrt{26} (ft/sec)$$

They are detaching from each other at a spped of $\sqrt{26}$ from each other.