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Answer:
y = 67.6 feet, y = 114.4/ (22 - 3t)
Explanation:
For this exercise let's use that light travels in a straight line and some trigonometric relationships, the symbols are in the attached diagram
Large triangle Projector up to the screen
tan θ = y / L
For the small triangle. Projector up to the person
tan θ = y₀ / (L-d)
The angle is the same, so we equate the two equations
y₀ / (L -d) = y / L
y = y₀ L / (L-d)
The distance from the screen (d), we look for it with kinematics
v = d / t
d = v t
we replace
y = y₀ L / (L - v t)
y = 5.2 22 / (22 - 3 t)
y = 114.4 (22 - 3t)⁻¹
This is the equation of the shadow height change as a function of time
For the suggested distance the shadow has a height of
y = 114.4 / (22-13)
y = 67.6 feet
The work done against gravity is 100 J
Explanation:
The work done against gravity in order to lift an object is equal to the change in gravitational potential energy of the object:

where
m is the mass of the object
g is the acceleration of gravity
is the change in height of the object
For the object in this problem, we have:
m = 5 kg


Substituting into the equation,

Learn more about work:
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Homogeneity and isotropy, On large enough scales, the Universe looks pretty much the same in all directions. The big bang theory is based on two assumptions: the first is centered around Einstein's general theory of relativity, which accurately describes gravity and the interactions of matter; and the second, also known as the cosmological principle, asserts that the universe is homogeneous and isotropic on a large enough scale.
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