Answer:
C) Check that the numerical answer is reasonable and the units are what you expected.
Explanation:
Answer: vf = 51 m/s
d = 112 m
Explanation: Solution attached:
To find vf we use acceleration equation:
a = vf - vi / t
Derive to find vf
vf = at + vi
Substitute the values
vf = 3.5 m/s² ( 8.0 s) + 23 m/s
= 51 m/s
To solve for distance we use
d = (∆v)² / 2a
= (51 m/s - 23 m/s )² / 2 ( 3.5 m/s²)
= (28 m/s)² / 7 m/s²
= 784 m/s / 7 m/s²
= 112 m
A. 
The orbital speed of the clumps of matter around the black hole is equal to the ratio between the circumference of the orbit and the period of revolution:

where we have:
is the orbital speed
r is the orbital radius
is the orbital period
Solving for r, we find the distance of the clumps of matter from the centre of the black hole:

B. 
The gravitational force between the black hole and the clumps of matter provides the centripetal force that keeps the matter in circular motion:

where
m is the mass of the clumps of matter
G is the gravitational constant
M is the mass of the black hole
Solving the formula for M, we find the mass of the black hole:

and considering the value of the solar mass

the mass of the black hole as a multiple of our sun's mass is

C. 
The radius of the event horizon is equal to the Schwarzschild radius of the black hole, which is given by

where M is the mass of the black hole and c is the speed of light.
Substituting numbers into the formula, we find
