Asked by Ribie
Derivatives - chain rule
An airplane, flying horizontally at an altitude of 1 mile, passes directly over an observer. If the constant speed of the airplane is 400 miles per hour, how fast is its distance from the observer increasing 45 seconds later? Hint: note that in 45 seconds (3/4 * 1/60 = 1/80), the airplane goes 5 miles.
An airplane, flying horizontally at an altitude of 1 mile, passes directly over an observer. If the constant speed of the airplane is 400 miles per hour, how fast is its distance from the observer increasing 45 seconds later? Hint: note that in 45 seconds (3/4 * 1/60 = 1/80), the airplane goes 5 miles.
Answers
Answered by
Steve
the distance z is found using
z^2 = 1^2 + x^2
at x=5, z^2 = 26
z dz/dt = x dx/dt
so at the moment in question
√26 dz/dt = 5*400
note that z will be in mi/hr
z^2 = 1^2 + x^2
at x=5, z^2 = 26
z dz/dt = x dx/dt
so at the moment in question
√26 dz/dt = 5*400
note that z will be in mi/hr
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