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
0"
(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.
0"
a) At what height will a 150-pound object weigh 50 pounds?
I used the following:"w = 150 w(h)= 50 r=3950
0"
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 break down the problem step by step.
First, let's represent the weight of the whelk on the surface of the Earth as "w". Since we don't know the exact weight of the whelk, we can leave it as a variable for now.
Next, we need to determine the weight change. The weight change is given as a percentage, so we'll represent it as 0.1% or 0.001.
Now, let's set up the equation to solve for the height. We'll use the formula provided:
w(h) = (r / (r + h))^2 * w
Since we want to find the height at which the weight changes by 0.1%, we can represent the new weight as (1 + 0.001) * w.
Plugging in these values, we get:
(1 + 0.001) * w = (r / (r + h))^2 * w
Next, we can simplify the equation by canceling out the "w" term on both sides:
1 + 0.001 = (r / (r + h))^2
Taking the square root of both sides to isolate r / (r + h), we get:
sqrt(1 + 0.001) = r / (r + h)
Now, we can solve for h by isolating it on one side:
r / (r + h) = sqrt(1 + 0.001)
Cross-multiplying, we get:
r = sqrt(1 + 0.001) * (r + h)
Expanding the equation, we have:
r = sqrt(1.001) * r + sqrt(1.001) * h
Simplifying further, we subtract sqrt(1.001) * r from both sides:
0 = sqrt(1.001) * h - sqrt(1.001) * r
Finally, dividing by sqrt(1.001) gives us the value of h:
h = (sqrt(1.001) * r) / sqrt(1.001)
Now, you can plug in the given value of r (3950 miles) and calculate the height at which the weight of the whelk changes by 0.1%.