For a homework project, some students constructed a model of the Moon orbiting the Earth to show the phases of the Moon.
The model was built upon a turntable with radius r, that rotates uniformly with an angular speed ω.
The students positioned LED lights to provide parallel incident light that represented light from the Sun.
The diagram shows the model as viewed from above.
The students noticed that the shadow of the model Moon could be seen on the wall.
At time t = 0, θ = 0 and the shadow of the model Moon could not be seen at position E as it passed through the shadow of the model Earth.
Some time later, the shadow of the model Moon could be seen at position X
(a)
For this model Moon and Earth
(i)
Construct an expression for θ in terms of ω and t
[1]
(ii)
Derive an expression for the distance EX in terms of r, ω and t
(iii)
Describe the motion of the shadow of the Moon on the wall
[1]