Question

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
weighs 115 lb. Find her weight when she is 271 mi above the surface of the earth and the spacecraft is not in motion.

Her weight is lbs.

(Round the answer to one decimal place.)

Answer 1

Answer:

100.8lb

Step-by-step explanation:

Firstly , we need to write the proportionality sign.

We were told weight is inversely proportional to distnace from earth's centre, this can be written as follows:

W ∝1/d^2

Removing the proportionality sign, and introducing the constant of proportionality yields:

W = k/d^2

W.d^2 = k

We now calculate the value of this constant as follows ;

115 × (3978)^2 = k

k = 1,819,815,660

We use this value now in calculating her weight above the surface of the earth.

We know she is 271mi above the earth's surface, her distance from the center of the earth would now be = 271 + 3978 = 4,249mi

We now use the relation again to calculate:

W.d^2 = k

w = k/d^2

w = 1,819,815,660/(4249)^2

w = 100.8 lb