Answer:
20min = 20 × 60 = 1200sec.
Speed in m per sec.
V = 1000/1200
V = 0.833m per sec.
Explanation:
Answer:
R = 103.7 N, 31.6° above x-axis
Explanation:
First we find the x components of all the forces:
F1x = F1 Cos 60°
F1x = (100 N)(Cos 60°)
F1x = 50 N
F2x = F2 Cos 140°
F2x = (200 N)(Cos 140°)
F2x = -153.2 N
F3x = F3 Cos 320°
F3x = (250 N)(Cos 320°)
F3x = 191.5 N
So, the x component of resultant will be the sum of the x component of each force:
Rx = F1x + F2x + F3x
Rx = 50 N - 153.2 N + 191.5 N
Rx = 88.3 N
Now we find the y components of all the forces:
F1y = F1 Sin 60°
F1y = (100 N)(Sin 60°)
F1y = 86.6 N
F2y = F2 Sin 140°
F2y = (200 N)(Sin 140°)
F2y = 128.5 N
F3y = F3 Sin 320°
F3y = (250 N)(Sin 320°)
F3y = -160.7 N
So, the y component of resultant will be the sum of the y component of each force:
Ry = F1y + F2y + F3y
Ry = 86.6 N + 128.5 N - 160.7 N
Ry = 54.4 N
Hence, the magnitude of resultant force will be:
|R| = √(Rx² + Ry²)
|R| = √[(88.3 N)² + (54.4 N)²]
|R| = √10756.25 N²
|R| = 103.7 N
And the direction θ will be:
θ = tan⁻¹(Ry/Rx)
θ = tan⁻¹(54.4/88.3)
θ = 31.6° above x-axis
Hence, the resultant vector will be:
<u>R = 103.7 N, 31.6° above x-axis</u>
Answer:
The index of refraction of the first medium must be higher than the index of refraction of the second medium
Explanation:
Snell's law describes the behaviour of light at the boundary between two mediums:
![n_1 sin \theta_1 = n_2 sin \theta_2](https://tex.z-dn.net/?f=n_1%20sin%20%5Ctheta_1%20%3D%20n_2%20sin%20%5Ctheta_2)
where
n1 and n2 are the index of refraction of the two mediums
are the angle between the direction of the light ray and the normal to the interface
We can rewrite the condition as:
![sin \theta_2 = \frac{n_1}{n_2} sin \theta_1](https://tex.z-dn.net/?f=sin%20%5Ctheta_2%20%3D%20%5Cfrac%7Bn_1%7D%7Bn_2%7D%20sin%20%5Ctheta_1)
Let's assume now that the light is travelling in the first medium with a very large angle with respect to the normal to the surface, i.e.
, so that
. In this case, we have
![sin \theta_2 = \frac{n_1}{n_2}](https://tex.z-dn.net/?f=sin%20%5Ctheta_2%20%3D%20%5Cfrac%7Bn_1%7D%7Bn_2%7D)
We notice that if
, the ratio on the right is larger than 1, and so the term
should be also larger than 1: but this is not possible of course, since the sine function is always less than 1. Therefore, in this case total internal reflection occurs, because no refracted ray is produced.
Answer:
(6.675 × 10⁶) m
Explanation:
A body vibrating in simple harmonic motion has its frequency related to the spring constant and mass of the body through the relation
f = (1/2π) √(k/m)
k = 2233 N/m
m = mass of one molecule of Nitrogen = 28.0 g = 0.028 kg
f = (1/2π) √(2233/0.028)
f = 44.945 Hz
And the photons that'll excite the molecule to the next state must at least have this frequency (f = 44.945 Hz)
For waves, the velocity (v), frequency (f) and wavelength (λ) are related through the relation
v = fλ
v = speed of light (since it's a photon) = (3 × 10⁸) m/s
λ = (v/f) = (3 × 10⁸)/44.945 = 6674824.8 m = (6.675 × 10⁶) m = (6.68 E6) m
Answer:
Explanation:
This is the case of horizontal projection from a height:
Time, t = sqrt ( 2h / g )
= sqrt ( 2 * 20 / 9.8 )
= 2.02 s
Vfx = V
Vfy = g* t = 2.02 g
theta (θ)= 45 deg
tan theta (tan θ) = Vfy / Vfx
tan 45 = 2.02 g / V
V = 2.02 * 9.8
= 19.8 m/s
≅ 20m/s