(a) Differentiate the position vector to get the velocity vector:
<em>r</em><em>(t)</em> = (3.00 m/s) <em>t</em> <em>i</em> - (4.00 m/s²) <em>t</em>² <em>j</em> + (2.00 m) <em>k</em>
<em>v</em><em>(t)</em> = d<em>r</em>/d<em>t</em> = (3.00 m/s) <em>i</em> - (8.00 m/s²) <em>t</em> <em>j</em>
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(b) The velocity at <em>t</em> = 2.00 s is
<em>v</em> (2.00 s) = (3.00 m/s) <em>i</em> - (16.0 m/s) <em>j</em>
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(c) Compute the electron's position at <em>t</em> = 2.00 s:
<em>r</em> (2.00 s) = (6.00 m) <em>i</em> - (16.0 m) <em>j</em> + (2.00 m) <em>k</em>
The electron's distance from the origin at <em>t</em> = 2.00 is the magnitude of this vector:
||<em>r</em> (2.00 s)|| = √((6.00 m)² + (-16.0 m)² + (2.00 m)²) = 2 √74 m ≈ 17.2 m
(d) In the <em>x</em>-<em>y</em> plane, the velocity vector at <em>t</em> = 2.00 s makes an angle <em>θ</em> with the positive <em>x</em>-axis such that
tan(<em>θ</em>) = (-16.0 m/s) / (3.00 m/s) ==> <em>θ</em> ≈ -79.4º
or an angle of about 360º + <em>θ</em> ≈ 281º in the counter-clockwise direction.
Answer:
Explanation:
The movement of a body can be analyzed using New's first law. In an inertial frame (without acceleration) every body is kept at rest or moving at constant speed until there is an external force that changes this state
Let's analyze these cases in the framework of this first law
a) If the vehicle is going at constant speed the two bodies (the egg and the hands) do not change movement so he had returned to the hands
b) If the vehicle accelerates the passenger goes faster, but the egg that is not subject to anything does not change the movement, so it falls behind the passenger
c) If the vehicle slows down, the passenger reduces its speed and the distance traveled in time, but the egg that is not attached follows its movement and falls in front of the passenger.
Answer:
Explanation:
thickness of oil t = 200 nm
index of refraction μ = 1.5
For transmitted light :---
path difference = 2μ t
For constructive interference
path difference = n λ , λ is wavelength of light
2μ t = n λ
λ = 2μ t / n
For longest λ , n = 1
λ = 2μ t
= 2 x 1.5 x 200 nm
= 600 nm
Wavelength in water
= 600 / refractive index of water
= 600 / 1.33
= 451.1 nm Ans
First thing to do is to draw the system described above. Then, write an equation for the forces present.
<span>
</span>Σ<span>F = Fg - Ff
</span><span>0 = mgsin</span><span>∅</span><span> - umgcos</span><span>∅</span><span>0 = gsin</span><span>∅</span><span> - ugcos</span><span>∅</span><span>
u = tan</span><span>∅
</span>∅(max) = tan^-1 (u)<span>
</span>
