The amount of gravitational potential energy acquired by the rock is equal to:

where
m is the mass of the rock
g is the gravitational acceleration

is the increase in height of the rock
Substituting the data of the problem, we find

So, Natalie gave 220.7 J of energy to the rock.
ANSWER:
The study and analysis of light according to its component wavelengths is called spectroscopy.
EXPLANATION:
Spectroscopy is the branch of science that is concerned with the investigation and measurement of spectrum produced when matter interacts with or emits electromagnetic radiation.It helps us to identify atoms and molecules in the object.Spectroscopy is used to find out Dopplers effect (the red shift and blue shift),which tells how fast the object is comming towards earth or moving away from the earth.
Hi there!
We can begin by solving for the linear acceleration as we are given sufficient values to do so.
We can use the following equation:
vf = vi + at
Plug in given values:
4 = 9.7 + 4.4a
Solve for a:
a = -1.295 m/s²
We can use the following equation to convert from linear to angular acceleration:
a = αr
a/r = α
Thus:
-1.295/0.61 = -2.124 rad/sec² ⇒ 2.124 rad/sec² since counterclockwise is positive.
Now, we can find the angular displacement using the following:
θ = ωit + 1/2αt²
We must convert the initial velocity of the tire (9.7 m/s) to angular velocity:
v = ωr
v/r = ω
9.7/0.61 = 15.9 rad/sec
Plug into the equation:
θ = 15.9(4.4) + 1/2(2.124)(4.4²) = 20.56 rad