Question

please help!!
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 124 lb. Find her weight when she is 123 mi above the surface of the earth and the spacecraft is not in motion. What is her weight ???

Answer 1

inverse square relation :
\[w=m \times \frac{ 1 }{ r^{2} }\]
you can calculate the mass by comparing weight and r at sea level,
then use the mass and 123 mi above to get the second weight.

Answer 2

i still cant figure it out

Answer 3

put into the equation the data that is given (first scenario, sea level):
use the formula above

Answer 4

first scenario:
\[124 lb = m \frac{ 1 }{ r^{2} }\]

Answer 5

do you know what is the distance from the center of the earth
in the first scenario?
r=

Answer 6

3978

Answer 7

and the weight was 124 lb, so we have:
\[124lb=m \times \frac{1}{ 3978 ^{2} }\]
mass is always the same, however, weight depends on gravity as well

Answer 8

ok

Answer 9

now we can solve for the mass by multiplying with 3978^2:
\[124 \times 3978^{2} = m\]

Answer 10

986544

Answer 11

and then we look at the second scenario (above sea level):
\[w = m \times \frac{ 1 }{ r^{2} }\]
this time we are 123 mi ABOVE sea level, so 123 mi higher than before.
the mass is the same (astronaut has not changed).
formula:
\[w = 986544 \times \frac{ 1 }{ (3978+123)^{2} }\]

Answer 12

I got 116,6733

Answer 13

lbs for the weight (with calculator)

Answer 14

i didnt idk what i did wrong

Answer 15

986544x4101^2

Answer 16

i got 8091633888

Answer 17

i need her in space

Answer 18

the site was unresponsive

yes you need her in space, that is why you add to the sea level
another 123 mi

Answer 19

we had
\[124 \times 3978^{2}\]
the result is
124 x 15824484 = 1962236016

Answer 20

oh ok

Answer 21

and then you DIVIDE that by 1401^2

Answer 22

ok then what do i do

Answer 23

1962236016 / 4101^2

Answer 24

700298.4

Answer 25

the mass (1962236016) is the SAME,
the distance from earth is now 4101 instead of 3978

Answer 26

no, thats too much...

Answer 27

mass (1962236016) divided by 1401^2=16818201

Answer 28

weight = 1962236016/1401^2

Answer 29

the numbers are very big because the distance from earth is so high

Answer 30

from the center of the earth

Answer 31

but 16818201 isnt her weight is it?

Answer 32

no, 16818201 was just the new distance=1401 squared
sorry if it's so confusing!

Answer 33

lol its fine so whats next

Answer 34

so that's what we divide the mass number 1962236016 with

Answer 35

116.67

Answer 36

YES

Answer 37

weight = 1962236016/1401^2 = 116.67 lbs when 123 mi above sea level

Answer 38

rounded to the nearest tenth is 116.7??

Answer 39

the weight decreased because earth has less power pulling her down
when she already got away from the center more

Answer 40

yes

Answer 41

116.7 isnt right

Answer 42

when i typed it in it said it was wrong

Answer 43

nvm thats right i was supossed to round to the hundreth thanks so mch

Answer 44

then I am relieved ! :D

your welcome