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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