The
horizontal component of an angular distance can be calculated by multiplying the
distance with the cosine of the angle, Dx = D * cos θ
While
the vertical component is calculated by multiplying the distance with the sine
of the angle, Dy = D * sin θ
The
resultant displacement can then be obtained using the formula for hypotenuse
and summations of each component:
R^2
= (summation of Dx)^2 + (summation of Dy)^2
summation
of Dx = 600 * cos47 + 500 * cos128 + 300 * cos209 + 400 *
cos(-77) = -71.0372
summation of Dy = 600 * sin47
+ 500 * sin128 + 300 * sin209 + 400 * sin(-77) = 297.6267
<span> Note: you have to draw the lines to correctly
determine the angles</span>
R^2 = (-71.0372)^2 + 297.6267^2
R = 306 m
The resultant angle is:
tan θ = Dy / Dx
θ =
tan^-1 (297.6267 / -71.0372)
θ =
103˚ = [N 13˚ W]
Therefore
displacement is 306 m <span>[N 13˚ W].</span>
Answer:
Explanation:
The magnitude of the acceleration makes an angle of 30° with the tangential velocity.
Resolving the acceleration to tangential and radial acceleration
at = aCos30 = √3a/2
ar = aSin30 = ½a
a = 2•ar
Then, the tangential acceleration is the linear acceleration, so the relationship between the tangential acceleration and angular acceleration is given as:
at = Rα
Then, α = at/R
since at = √3a/2
Then, α = √3 at/2R, equation 1
The radial acceleration is given as
ar = ω²R
Note that, at² + ar² = a²
at = √(a²-ar²)
Back to equation 1
α = √3 at/2R
α = √3√(a²-ar²)/2R
α = √3√(a²-(w²R)²)/2R
α = √3(a²-w⁴R²) / 2R
Also, a = 2•ar = 2w²R
Then,
α = √3((2w²R)²-w⁴R²) / 2R
α = √3(4w⁴R²-w⁴R²) / 2R
α = √3(3w⁴R²) / 2R
α = √9w⁴R² / 2R
α = 3w²R / 2R
α = 3w²/2
Potential Energy (P.E) = Mass x
Acceleration due to Gravity x Altitude. Putting this value in the above equation we get, Dimensional Formula of
Potential energy= M1L2T-2.
Answer: No
Explanation:
Whenever light travelling on a straight line encounters obstruction, it diffracts and scatter.
Scattering of light occurs when light passes through a rough path or a diffused surface.
But in case of spectral diffusion, which is the fluctuation in spectroscopy as a result of time dependent frequency shifts.
Spectral diffusion occurs in particular molecules initiated by excessive excitation energy.
Fluctuation in frequency does not mean diffraction of light or particles
Therefore, spectral diffusion does not cause light to scatter.
