Another aeronautics problem

**explodingtoenails** · August 13th 2011, 03:34 PM

A hot air balloon rises at the rate of 70 feet per minute. An observer 410 feet from the place of ascent watches the balloon rise.

a) Write an expression for the altitude of the balloon in terms of time, t minutes, and the angle of elevation, theta.

b) What is the altitude of the balloon after 3.5 minutes, 22 minutes, and 1 hour?

c) What are the angles of elevation to the nearest minute for each amount of time?

I can only figure out how to make an equation for a), not an expression. I know how to do b) but I don't know how to get the angles of elevation for each time.

**e^(i*pi)** · August 13th 2011, 03:46 PM

For the first part your equation will be the product of the height rise multiplied by time multiplied by the appropriate trig ratio

Once you have part A done part B and C are simpler.

**explodingtoenails** · August 13th 2011, 11:55 PM

Part a) asks for an expression, not an equation. That's what I'm having big trouble with.

**earboth** · August 14th 2011, 12:03 AM

Originally Posted by explodingtoenails

A hot air balloon rises at the rate of 70 feet per minute. An observer 410 feet from the place of ascent watches the balloon rise.

a) Write an expression for the altitude of the balloon in terms of time, t minutes, and the angle of elevation, theta.

...

Originally Posted by explodingtoenails

Part a) asks for an expression, not an equation. That's what I'm having big trouble with.

As far as I understand the question you are asked to write 2 (two) "expressions": The 1st one wrt time, the 2nd one wrt the angle:

Referring to e^(i*pi)'s post in both cases you have to "express" the value of h:

$\overbrace{h(t)=\underbrace{70 \cdot h}_{expression}}^{equation}$

$\overbrace{h(\theta)=\underbrace{410 \cdot \tan(\theta)}_{expression}}^{equation}$

**Istafa** · August 14th 2011, 01:22 AM

The altitude is simple,
$a(t)=70t$
where altitude is in feet and t in minutes
now, using the tan trig ratio:
$\tan(\theta)=\frac{a}{410}$
$a(\theta)=410\tan(\theta)$
Now, calculate a(3.5), a(22) and a(60) for the answer to b using first equation
now from the above equations:
$70t=410\tan(\theta)$
$\theta=\arctan(\frac{70t}{410})$
Now sub in the values of time to work out angles of elevation

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