Answer:
0.30 m/s²
Explanation:
Given:
v₀ = 0.2 m/s
v = 1.6 m/s
t = 4.7 s
Find: a
a = (v − v₀) / t
a = (1.6 m/s − 0.2 m/s) / 4.7 s
a = 0.30 m/s²
The axial field is the integration of the field from each element of charge around the ring. Because of symmetry, the field is only in the direction of the axis. The field from an element ds in the ring is
<span>dE = (qs*ds)cos(T)/(4*pi*e0)*(x^2 + R^2) </span>
<span>where x is the distance along the axis from the plane of the ring, R is the radius of the ring, qs is the linear charge density, T is the angle of the field from the x-axis. </span>
<span>However, cos(T) = x/sqrt(x^2 + R^2) </span>
<span>so the equation becomes </span>
<span>dE = (qs*ds)*[x/sqrt(x^2 + R^2)]/(4*pi*e0)*(x^2 + R^2) </span>
<span>dE =[qs*ds/(4*pi*e0)]*x/(x^2 + R^2)^1.5 </span>
<span>Integrating around the ring you get </span>
<span>E = (2*pi*R/4*pi*e0)*x/(x^2 + R^2)^1.5 </span>
<span>E = (R/2*e0)*x*(x^2 + R^2)^-1.5 </span>
<span>we differentiate wrt x, the term R/2*e0 is a constant K, and the derivative is </span>
<span>dE/dx = K*{(x^2 + R^2)^-1.5 +x*[(-1.5)*(x^2 + R^2)^-2.5]*2x} </span>
<span>dE/dx = K*{(x^2 + R^2)^-1.5 - 3*x^2*(x^2 + R^2)^-2.5} </span>
<span>to find the maxima set this = 0, giving </span>
<span>(x^2 + R^2)^-1.5 - 3*x^2*(x^2 + R^2)^-2.5 = 0 </span>
<span>mult both side by (x^2 + R^2)^2.5 to get </span>
<span>(x^2 + R^2) - 3*x^2 = 0 </span>
<span>-2*x^2 + R^2 = 0 </span>
<span>-2*x^2 = -R^2 </span>
<span>x = (+/-)R/sqrt(2) </span>
Answer: The incident ray and the reflected ray and the normal will be parallel to each other.
Explanation:
The normal is perpendicular to the surface of the mirror or the reflective surface.
According to the law of reflection which state that:
The angle of incidence is always equal to the angle of reflection on a smooth surface.
If a light ray is incident on a reflective surface along the normal. The angle of incidence will be at 90 degrees which will be perpendicular to the surface of the mirror, the reflected ray will bounce back likewise at the same angle which will be perpendicular to the reflective surface.
Both the incident ray and the reflected ray and the normal will be parallel to each other.
I think the correct answer from the choices listed above is option D. Scientific theories summarize patterns found in nature. Although, the statement scientific theories are never proven is somewhat true. They are either disproved or they are never disproved. Hope this answers the question.
