Can someone please help me with the following question.
1) The weight of an object above Earth can be modeled by a function of the form w(h)=(r/r+h)^2*"w , where r is the radius of Earth
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(approximately 3950 miles)," h" is the distance above Earth's surface, and
"w is the weight of the object on the surface of the Earth.
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a) At what height will a 150-pound object weigh 50 pounds?
I used the following:"w = 150 w(h)= 50 r=3950
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So I plugged these values into the equation given:
50=(3950/3950 + h)^2*150
and my answer was h= 7900
b) How high would a crow carrying a whelk haveto fly for the whelk's weight to change by 0.1%?
To solve part b) of the question, we need to find the height at which the weight of the whelk changes by 0.1%.
Let's first establish the given information:
- The weight of the whelk on the surface of the Earth (w) is not mentioned, so we'll leave it as a variable.
- The weight at a certain height (w(h)) can be modeled by the equation: w(h) = (r / r + h)^2 * w
- The weight change is indicated as 0.1%, which can be expressed as 0.001 (1% = 0.01).
Now, let's set up the equation using the given information:
w(h) = (r / r + h)^2 * w
w(h) + 0.001 * w = w
Since 0.001 * w is the weight change, we can rewrite the equation as:
w(h) + 0.001 * w = w + 0.001 * w
Now, we can simplify the equation:
w(h) = 0.001 * w
We can substitute the equation of w(h) from part a) into this simplified equation:
(3950 / 3950 + h)^2 * w = 0.001 * w
Canceling out the w term from both sides:
(3950 / 3950 + h)^2 = 0.001
Taking the square root of both sides to isolate the h term:
3950 / (3950 + h) = √0.001
Square both sides of the equation to eliminate the square root:
(3950 / (3950 + h))^2 = 0.001
Cross multiply and simplify:
3950^2 = 0.001 * (3950 + h)^2
Simplify further:
(3950 + h)^2 = (3950^2) / 0.001
Take the square root of both sides to find the value of (3950 + h):
3950 + h = √((3950^2) / 0.001)
Subtract 3950 from both sides:
h = √((3950^2) / 0.001) - 3950
Using a calculator, you can find the value of h.