# Thread: [SOLVED] Related rates problem for calculus

1. ## [SOLVED] Related rates problem for calculus

A hot-air balloon is rising straight up from a level field and is tracked by a range finder 500 ft from lift-off point. the balloon rises at a rate of 15 feet per second.

A) How fast is the direct distance between the range finder and the ballon changing at 5 seconds

B) how fast is the angle of elevation changing when the ballon is 500 feet high

he gave us a diagram of a right trianle with the hypotenus labeled d and the side labled h and the bottom equalling 500

2. Originally Posted by ballet_dansur13
A hot-air balloon is rising straight up from a level field and is tracked by a range finder 500 ft from lift-off point. the balloon rises at a rate of 15 feet per second.

A) How fast is the direct distance between the range finder and the ballon changing at 5 seconds

B) how fast is the angle of elevation changing when the ballon is 500 feet high

he gave us a diagram of a right trianle with the hypotenus labeled d and the side labled h and the bottom equalling 500
also label the angle of elevation something. say $\displaystyle \theta$

Then we have the following relationship using trig ratios:

$\displaystyle \cos \theta = \frac {500}d$

that is,

$\displaystyle \cos \theta = 500d^{-1}$

now differentiate implicitly with respect to t (time) and continue (can you?)