# Thread: A balloon rising?

1. ## A balloon rising?

"A balloon is rising vertically above a level, straight road at a constant rate of 4 ft/sec. Just when the balloon is 56 feet above the ground, a bicycle moving at a constant rate of 17 ft/sec passes under it.

a) How fast is the distance s(t) between the bicycle and the balloon increasing 3 seconds later?

b) How fast is the angle between y(t) and s(t) changing at that time?"

2. Originally Posted by JessicaWade
"A balloon is rising vertically above a level, straight road at a constant rate of 4 ft/sec. Just when the balloon is 56 feet above the ground, a bicycle moving at a constant rate of 17 ft/sec passes under it.

a) How fast is the distance s(t) between the bicycle and the balloon increasing 3 seconds later?

b) How fast is the angle between y(t) and s(t) changing at that time?"
(a) $\displaystyle s^2 = (17t)^2 + (56+4t)^2$

find $\displaystyle \frac{ds}{dt}$ at t = 3

(b) $\displaystyle \tan{\theta} = \frac{17t}{56+4t}$

find $\displaystyle \frac{d\theta}{dt}$ at t = 3