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November 3rd, 2019, 10:12 PM   #1
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Rates of change

Please help me with this!

A rocket, rising vertically, is tracked by a radar station that is on the ground 5km from the Launchpad.How fast is the rocket rising when it is 4km high and its distance from the radar station is increasing at a rate of 200 km/h?
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November 3rd, 2019, 10:49 PM   #2
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as a matter of notation $\dot{f} = \dfrac{df}{dt}$

$r^2 = 5^2 + h^2= 25 + h^2$

$2 r \dot{r} = 2h\dot{h}$

$\dot{h} = \dfrac{2r \dot{r}}{2 h} = \dfrac{r \dot{r}}{h}$

$\left . r \right|_{h=4} = \sqrt{25+16} = \sqrt{41}$

$\dot{r} = 200$

$h = 4$

you can finish
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