An airplane, flying horizontally at an altitude of 1 mile, passes directly over

Question

An airplane, flying horizontally at an altitude of 1 mile, passes directly over an observer. If the constant speed of the airplane is 480 miles per hour, how fast is its distance from the observer increasing 15 seconds later? Hint: Note that in 15 seconds ( 1/4 . 1/60 = 1.240 hour), hour , the airplane goes 2 miles. 15 seconds after the airplane has passed over, the distance from the observer is increasing at a rate of miles per hour. Round the final answer to the nearest integer as needed. Round all intermediate values to the nearest thousandth as needed.)

Explanation / Answer

draw a right triangle:

base = x = 2 miles (changing)

height = h = 1 mile (constant)

hypotenuse = d = sqrt5 miles (changing)

equation:

x^2 + 1^2 = d^2

differentiate:

2x (dx/dt) + 0 = 2d (dd/dt)

plug and solve:

2(2)(480) = 2(sqrt5)(dd/dt)

960 = sqrt(5)dd/dt

dd/dt = 960/sqrt5 miles/hr

bol

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