the moderate temperatures of islands throughout the world has much to do with water's vast supply of internal energy. high evapo
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Answer: The length of the shadow on the wall is decreasing by 0.6m/s
Explanation:
the specified moment in the problem, the man is standing at point D with his head at point E.
At that moment, his shadow on the wall is y=BC.
The two right triangles ΔABC and ΔADE are similar triangles. As such, their corresponding sides have equal ratios:
ADAB=DEBC
8/12=2/y,∴y=3 meters
If we consider the distance of the man from the building as x then the distance from the spotlight to the man is 12−x.
(12−x) /12=2/y
1− (1 /12x )=2 × 1/y
Let's take derivatives of both sides:
−1 / 12dx = −2 × 1 / y^2 dy
Let's divide both sides by dt:
−1/12⋅dx/dt=−2/y^2⋅dy/dt
At the specified moment:
dxdt=1.6 m/s
y=3
Let's plug them in:
−1/121.6) = - 2/9 × dy/dt
dy/dt = 1.6/12 ÷ 2/9
dy/dt = 1.6/12 × 9/2
dy/dt = 14.4/24 = 0.6m/s
Answer:
- Yes.
Explanation:
A particular solution for the 1D wave equation has the form
where A its the amplitude, k the wavenumber, ω the angular frequency and φ the phase angle.
Now, for any given position , we can use:
so, the equation its:
.
This is the equation for a simple harmonic oscillation!
So, for any given point, we can use a simple harmonic oscillation as visual model. Now, when we move a distance from the original position, we got:
and
now, this its
So, there its a phase angle difference of . We can model this simply by starting the simple harmonic oscillation with a different phase angle.