Answer:
The resultant velocity is <u>169.71 km/h at angle of 45° measured clockwise with the x-axis</u> or the east-west line.
Explanation:
Considering west direction along negative x-axis and north direction along positive y-axis
Given:
The car travels at a speed of 120 km/h in the west direction.
The car then travels at the same speed in the north direction.
Now, considering the given directions, the velocities are given as:
Velocity in west direction is, ![\overrightarrow{v_1}=-120\ \vec{i}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv_1%7D%3D-120%5C%20%5Cvec%7Bi%7D)
Velocity in north direction is, ![\overrightarrow{v_2}=120\ \vec{j}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv_2%7D%3D120%5C%20%5Cvec%7Bj%7D)
Now, since
are perpendicular to each other, their resultant magnitude is given as:
![|\overrightarrow{v_{res}}|=\sqrt{|\overrightarrow{v_1}|^2+|\overrightarrow{v_2}|^2}](https://tex.z-dn.net/?f=%7C%5Coverrightarrow%7Bv_%7Bres%7D%7D%7C%3D%5Csqrt%7B%7C%5Coverrightarrow%7Bv_1%7D%7C%5E2%2B%7C%5Coverrightarrow%7Bv_2%7D%7C%5E2%7D)
Plug in the given values and solve for the magnitude of the resultant.This gives,
![|\overrightarrow{v_{res}}|=\sqrt{(120)^2+(120)^2}\\\\|\overrightarrow{v_{res}}|=120\sqrt{2} = 169.71\ km/h](https://tex.z-dn.net/?f=%7C%5Coverrightarrow%7Bv_%7Bres%7D%7D%7C%3D%5Csqrt%7B%28120%29%5E2%2B%28120%29%5E2%7D%5C%5C%5C%5C%7C%5Coverrightarrow%7Bv_%7Bres%7D%7D%7C%3D120%5Csqrt%7B2%7D%20%3D%20169.71%5C%20km%2Fh)
Let the angle made by the resultant be 'x' degree with the east-west line or the x-axis.
So, the direction is given as:
![x=\tan^{-1}(\frac{|v_2|}{|v_1|})\\\\x=\tan^{-1}(\frac{120}{-120})=\tan^{-1}(-1)=-45\ deg(clockwise\ angle\ with\ the\ x-axis)](https://tex.z-dn.net/?f=x%3D%5Ctan%5E%7B-1%7D%28%5Cfrac%7B%7Cv_2%7C%7D%7B%7Cv_1%7C%7D%29%5C%5C%5C%5Cx%3D%5Ctan%5E%7B-1%7D%28%5Cfrac%7B120%7D%7B-120%7D%29%3D%5Ctan%5E%7B-1%7D%28-1%29%3D-45%5C%20deg%28clockwise%5C%20angle%5C%20with%5C%20the%5C%20x-axis%29)
Therefore, the resultant velocity is 169.71 km/h at angle of 45° measured clockwise with the x-axis or the east-west line.
Answer:
The wavelength of this wave is 1.01 meters.
Explanation:
The variation in the pressure of helium gas, measured from its equilibrium value, is given by :
..............(1)
The general equation is given by :
...........(2)
On comparing equation (1) and (2) :
![k=6.2](https://tex.z-dn.net/?f=k%3D6.2)
Since, ![k=\dfrac{2\pi}{\lambda}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B2%5Cpi%7D%7B%5Clambda%7D)
![\dfrac{2\pi}{\lambda}=6.2](https://tex.z-dn.net/?f=%5Cdfrac%7B2%5Cpi%7D%7B%5Clambda%7D%3D6.2)
![\lambda=1.01\ m](https://tex.z-dn.net/?f=%5Clambda%3D1.01%5C%20m)
So, the wavelength of this wave is 1.01 meters. Hence, this is the required solution.
Answer:
Explanation:
a )
Energy stored by left spring when compressed = 1/2 k x²
= .5 x 10 x .02² = .002 J .
Let compression in right spring = y
energy stored to right spring = 1/2 k y²
1/2 k y² = 0.002
.5 x 20 x y² = 0.002
y = .01414 m
= 1.4 cm
Answer:
Oligopoly
Explanation:
An oligopoly is the structure of the market that is characterized by the domination of a few firms or industries. Other small firms also operate in the same market, but the power concentration is associated with few firms only. Interdependency among the firms helps in planning and strategy making to introduce new ideas to increase the market activities. The competition in the market is reduced when a few of the firms dominate the market. It results in an increase in the price of commodities.