Hello, Super Mallow!
I use a slightly different set-up . . .
2) A balloon is rising vertically above a level, straight road at a constant rate of 1 ft/sec.
Just when the balloon is 65 feet about the ground,
a bicycle moving at a constant rate of 17 ft/sec passes under it.
How fast is the distance s(t) between the bicycle and the balloon increasing 3 sec later?
t ↑ \
↑ \ s(t)
P * \
65 | \
* → → → → *
A 17t C
The balloon is at when the cycle passes under it (at ): .
In the next seconds, the balloon rises feet to point : .
In the same seconds, the bicycle moves feet to point : .
Using Pythagorus: .
Differentiate with respect to time:
And now let