# calculus

"superman is in level flight 6 miles above ground. his flight plan takes him directly over whs high school. how fast is he flying when the distance between him and the whs high school is exactly 10 miles and the rate is increasing 40mph?"

i keep getting:

r = 10
r'=40
y=6
x=8
x'=50

but that is impossible since the derivative of x is still a leg of a right triangle and that it cannot be increasing faster than the hypotenuse. please help me i cannot find the answer.
reiny said:
Let his horizontal distance over the high school be x
let the distance between him and the school be y

I see a right-angled triangle and
x^2 + 6^2 = y^2

2x dx/dt + 0 = 2y dy/dt , #1

when x = 10, y^2 = 100 + 36, y = √136

in equation #1
2(10) dx/dt = 2(√136) (40)
dx/dt = 40√136/10
= 4√4 √ 34
= 8√34 mph or appr 46.65 mph

but if y = distance between him and school then y should = 10 and 8 should = 8, i am confused by the answer you gave me.

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1. typo: 8 should = 8

i meant x should = 8

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posted by eric
2. You are right, I subbed 10 into the wrong variable
Good catch.

when y = 10
x^2+ 6^2 = 10^2
x^2 =100-36= 64
x = √64 = 8

in my #1 from above post:

2(8) dx/dt = 2(10)(40)
dx/dt = 50 mph

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posted by Reiny

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