Calcuslus-Calculus-Calculus

A rocket arises from its launching pad with a velocity given. By 0.1 h m/s ,where h m is the height reached by the rocket at that time.the rocket is obserrvved from 2000 m away from the launch pad.at. What rate is the distance of the roocket from observer channging when the rocket is at an altitude of 5000 m?
The answer is suppose to be 464 m/s and please provide the whole procedure .Thanks.

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  1. Did you make a diagram?
    let the height be h m
    let the distance between rocket and observer be d m
    then
    d^2 = h^2 + 2000^2
    2 d dd/dt = 2h dh/dt = 0
    dd/dt = (h/d) dh/dt

    when h=5000 from first equation
    d = 5385.165

    dd/dt = (5000/5385.164)(5000(.1)) = 464.238

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  2. Thank you and yea i tried it but i was makin a minor mistake and now i see it .

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