Answer:
6.0 m/s
Explanation:
According to the law of conservation of energy, the total mechanical energy (potential, PE, + kinetic, KE) of the athlete must be conserved.
Therefore, we can write:
or
where:
m is the mass of the athlete
u is the initial speed of the athlete (at the bottom)
0 is the initial potential energy of the athlete (at the bottom)
v = 0.80 m/s is the final speed of the athlete (at the top)
is the acceleration due to gravity
h = 1.80 m is the final height of the athlete (at the top)
Solving the equation for u, we find the initial speed at which the athlete must jump:
Answer: The unpolarized light's intensity is reduced by the factor of two when it passes through the polaroid and becomes linearly polarized in the plane of the Polaroid. When the polarized light passes through the polaroid with the plane of polarization at an angle 
with respect to the polarization plane of the incoming light, the light's intensity is reduced by the factor of 
(this is the Law of Malus).
Explanation: Let us say we have a beam of unpolarized light of intensity 
that passes through two parallel Polaroid discs with the angle of between their planes of polarization. We are asked to find such that the intensity of the outgoing beam is 
. To solve this we follow the steps below:
Step 1. It is known that when the unpolarized light passes through a polaroid its intensity is reduced by the factor of two, meaning that the intensity of the beam passing through the first polaroid is
This beam also becomes polarized in the plane of the first polaroid.
Step 2. Now the polarized beam hits the surface of the second polaroid whose polarization plane is at an angle with respect to the plane of the polarization of the beam. After passing through the polaroid, the beam remains polarized but in the plane of the second polaroid and its intensity is reduced, according to the Law of Malus, by the factor of 
This yields 
. Substituting from the previous step we get
yielding
and finally,
