# A balloon rising?

• Oct 20th 2009, 02:59 PM
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?"
• Oct 20th 2009, 03:12 PM
skeeter
Quote:

(a) $s^2 = (17t)^2 + (56+4t)^2$
find $\frac{ds}{dt}$ at t = 3
(b) $\tan{\theta} = \frac{17t}{56+4t}$
find $\frac{d\theta}{dt}$ at t = 3