could you please show every formula and values used A free-fall experiment is pe
ID: 1492651 • Letter: C
Question
could you please show every formula and values used
A free-fall experiment is performed on a newly discovered spherical planetoid ("planet X"). where an 80 kg astronaut dropped a rock from a height of 216 cm and its falling time was electronically measured to be 1.0392 sec. The planet's circumference was determined to be 36.74 times 10^6 m by geometrical methods. The astronaut is fully aware that h = 1/2 g t^2. Determine the following. a) The weight of the astronaut on the planet's surface: b) The mass M of planet X:Explanation / Answer
As per given data
h = (1/2)gt^2
2.16m= (1/2)g(1.0392)^2
g = 2*2.16 m / (1.0392)^2
= 4 m/s^2
w = mg = ( 80)( 4) = 320 N
(b)
circumperence = 2 pi r
r = 36.74 * 10^6 m/ 2 pi
=5.85 * 10^6 m
from the Universal gravitatonal law
F = G m1 m2/r^2
320 N = 6.67 * 10^-11 ( 80) m2/ ( 5.85 * 10^6)^2
m2 = 20.52 * 10^23 kg
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