Trig derivative applications

May 2010
36
0
Hi,

I'm having trouble with the following two questions which are applications of trig derivatives:

1) A rocket is moving into the air with a height function given by \(\displaystyle h(t) = 200t^2\). A camera located 150 m away from the launch site is filming the launch. How fast must the angle of the camera be changing with respect to the horizontal 4 seconds after lift off?



2) The base of an isosceles triangle is 20 cm and the altitude is increasing at the rate of 1 cm/min. At what rate is the base angle increasing when the area is \(\displaystyle 100 cm^2?\)



I'm very confused with the two question
[/FONT][FONT=&quot]s, and am not even sure where to start. Any helpful tips/suggestions would be greatly appreciated..


Thanks :)
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skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
Hi,

I'm having trouble with the following two questions which are applications of trig derivatives:

1) A rocket is moving into the air with a height function given by \(\displaystyle h(t) = 200t^2\). A camera located 150 m away from the launch site is filming the launch. How fast must the angle of the camera be changing with respect to the horizontal 4 seconds after lift off?



2) The base of an isosceles triangle is 20 cm and the altitude is increasing at the rate of 1 cm/min. At what rate is the base angle increasing when the area is \(\displaystyle 100 cm^2?\)
1) let \(\displaystyle \theta\) = camera angle

\(\displaystyle \tan{\theta} = \frac{200t^2}{150}\)

take the time derivative and determine the value of \(\displaystyle \frac{d\theta}{dt}\) when \(\displaystyle t = 4\)

2) let \(\displaystyle \theta\) = base angle

\(\displaystyle h\) = altitude

\(\displaystyle \tan{\theta} = \frac{h}{10}\)

same drill ... take the time derivative and determine \(\displaystyle \frac{d\theta}{dt}\) when \(\displaystyle A = 100\)
 
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