November 3rd, 2019, 10:12 PM  #1 
Newbie Joined: Sep 2019 From: Papua New Guinea Posts: 13 Thanks: 1  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? 
November 3rd, 2019, 10:49 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,638 Thanks: 1473 
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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