Math 125-103
Fall 2012
Quiz 23, Oct. 26
Carter
Name
A hot air balloon rising straight up from a level field is tracked by a range finder 150 meters
from the liftoff point. At the moment that the range finder’s elevation angle is π/4, the angle is
increasing at the rate of 0.14 rad/min. How fast is the balloon rising at that moment?
Solution.
• Let θ denote the angle of inclination.
• Let y denote the vertical displacement.
• Given the lift-off point of the balloon is 150 meters from
the range finder.
• Given
• Find
dθ
dt |θ=π/4
= 014 rad/min.
dy
dt |θ=π/4 .
Evidently from the figure y = 150 tan (θ). Thus
150 meters
dy
dθ
= 150 sec2 (θ) .
dt
dt
At θ = π/4, we obtain:
dy
= 150 sec2 (π/4)0.14 = 150 · 2 · 0.14 = 300 · 0.14 = 3 · 14 = 42.
dt
The units are Meters per minute.