The weight W of an object varies inversely as the square of the distance d from the center of the earth. At sea level (3978 mi from the center of the earth), an astronaut weights is 110lb. Find her weight when she is 459 mi above the surface of the earth and the space craft is not in motion.
weight=110(3978/(459+3978))^2
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To solve this problem, we can use the inverse square relationship between weight and distance:
W = k/d^2
where W represents the weight, d represents the distance, and k is a constant.
Step 1: Find the value of k
We are given that the weight at sea level is 110 lb and the distance from the center of the Earth is 3978 mi. Let's substitute these values into the equation to find k:
110 = k/(3978)^2
Now, we can solve for k:
k = 110 * (3978)^2
k ≈ 1735696040
Step 2: Find the weight when the distance from the center of the Earth is 459 mi
Now that we have the value of k, we can use it to find the weight when the distance is 459 mi:
W = (1735696040)/(459)^2
W = 1735696040/210681
W ≈ 8238.41 lb
Therefore, the astronaut would weigh approximately 8238.41 lb when she is 459 mi above the surface of the Earth and the spacecraft is not in motion.
To solve this problem, we can use the inverse square law formula for variation:
W ∝ 1/d^2
where W is the weight of the object and d is the distance from the center of the earth.
From the given information, we know that at sea level (d = 3978 mi), the astronaut's weight (W) is 110 lb.
Now, let's use this information to find the constant of variation. We can set up the following equation:
W ∝ 1/d^2
110 ∝ 1/(3978)^2
To solve for the constant of variation, we can multiply both sides of the equation by (3978)^2:
110 * (3978)^2 = 1
Now, we have the constant of variation: (3978)^2 = 15,809,284.
Now, we can use this constant of variation to find the weight of the astronaut when she is 459 mi above the surface of the earth.
W ∝ 1/d^2
W ∝ 1/(459)^2
W ∝ 1/209,961
To get the weight (W), we can multiply 1/209,961 by the constant of variation:
W = (1/209,961) * 15,809,284
W ≈ 75.27 lb
Therefore, when the astronaut is 459 mi above the surface of the earth and the spacecraft is not in motion, her weight would be approximately 75.27 lb.