Answer:
Explanation:
Given
time taken ![t=2\ s](https://tex.z-dn.net/?f=t%3D2%5C%20s)
Speed acquired in 2 sec ![v=42\ m/s](https://tex.z-dn.net/?f=v%3D42%5C%20m%2Fs)
Here initial velocity is zero ![u=0](https://tex.z-dn.net/?f=u%3D0)
acceleration is the rate of change of velocity in a given time
![a=\frac{v-u}{t}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7Bv-u%7D%7Bt%7D)
![a=\frac{42-0}{2}=21\ m/s^2](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B42-0%7D%7B2%7D%3D21%5C%20m%2Fs%5E2)
Distance travel in this time
![s=ut+0.5at^2](https://tex.z-dn.net/?f=s%3Dut%2B0.5at%5E2)
where
s=displacement
u=initial velocity
a=acceleration
t=time
![s=0+\0.5\times 21\times (2)^2](https://tex.z-dn.net/?f=s%3D0%2B%5C0.5%5Ctimes%2021%5Ctimes%20%282%29%5E2)
![s=42\ m](https://tex.z-dn.net/?f=s%3D42%5C%20m)
so Jet Plane travels a distance of 42 m in 2 s
Answer:
Una secadora de cabello tiene una resistencia de 10Ω al circular una corriente de 6 Amperes, si está conectado a una diferencia de potencial de 120 V, durante 18 minutos ¿Qué cantidad de calor produce?, expresado en calorías
Answer:
- 278.34 kg m/s^2
Explanation:
The rate of the change of momentum is the same as the force.
The force that an object feels when moviming in a circular motion is given by:
F = -mrω^2
Where ω is the angular speed and r is the radius of the circumference
Aditionally, the tangential velocity of the body is given as:
v = rω
The question tells us that
v = 25 m/s
r = 7m
mv = 78 kg m/s
Therefore:
m = (78 kg m/s) / (25 m/s) = 3.12 kg
ω = (25 m/s) / (7 m) = 3.57 (1/s)
Now, we can calculate the force or rate of change of momentum:
F = - (3.12 kg) (7 m)(3.57 (1/s))^2
F = - 278.34 kg m/s^2
Answer:
From the question we are told that
The length of the rod is ![L_o](https://tex.z-dn.net/?f=L_o)
The speed is v
The angle made by the rod is ![\theta](https://tex.z-dn.net/?f=%5Ctheta)
Generally the x-component of the rod's length is
![L_x = L_o cos (\theta )](https://tex.z-dn.net/?f=L_x%20%3D%20%20L_o%20cos%20%28%5Ctheta%20%29)
Generally the length of the rod along the x-axis as seen by the observer, is mathematically defined by the theory of relativity as
![L_xo = L_x \sqrt{1 - \frac{v^2}{c^2} }](https://tex.z-dn.net/?f=L_xo%20%20%3D%20%20L_x%20%20%5Csqrt%7B1%20%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D)
=> ![L_xo = [L_o cos (\theta )] \sqrt{1 - \frac{v^2}{c^2} }](https://tex.z-dn.net/?f=L_xo%20%20%3D%20%20%5BL_o%20cos%20%28%5Ctheta%20%29%5D%20%20%5Csqrt%7B1%20%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D)
Generally the y-component of the rods length is mathematically represented as
![L_y = L_o sin (\theta)](https://tex.z-dn.net/?f=L_y%20%20%3D%20%20L_o%20%20sin%20%28%5Ctheta%29)
Generally the length of the rod along the y-axis as seen by the observer, is also equivalent to the actual length of the rod along the y-axis i.e
Generally the resultant length of the rod as seen by the observer is mathematically represented as
![L_r = \sqrt{ L_{xo} ^2 + L_y^2}](https://tex.z-dn.net/?f=L_r%20%20%3D%20%20%5Csqrt%7B%20L_%7Bxo%7D%20%5E2%20%2B%20L_y%5E2%7D)
=> ![L_r = \sqrt{[ (L_o cos(\theta) [\sqrt{1 - \frac{v^2}{c^2} }\ \ ]^2+ L_o sin(\theta )^2)}](https://tex.z-dn.net/?f=L_r%20%20%3D%20%5Csqrt%7B%5B%20%28L_o%20cos%28%5Ctheta%29%20%5B%5Csqrt%7B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D%5C%20%5C%20%5D%5E2%2B%20L_o%20sin%28%5Ctheta%20%29%5E2%29%7D)
=> ![L_r= \sqrt{ (L_o cos(\theta)^2 * [ \sqrt{1 - \frac{v^2}{c^2} } ]^2 + (L_o sin(\theta))^2}](https://tex.z-dn.net/?f=L_r%3D%20%5Csqrt%7B%20%28L_o%20cos%28%5Ctheta%29%5E2%20%2A%20%5B%20%5Csqrt%7B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D%20%5D%5E2%20%2B%20%28L_o%20sin%28%5Ctheta%29%29%5E2%7D)
=> ![L_r = \sqrt{(L_o cos(\theta) ^2 [1 - \frac{v^2}{c^2} ] +(L_o sin(\theta))^2}](https://tex.z-dn.net/?f=L_r%20%20%3D%20%5Csqrt%7B%28L_o%20cos%28%5Ctheta%29%20%5E2%20%5B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%5D%20%2B%28L_o%20sin%28%5Ctheta%29%29%5E2%7D)
=> ![L_r = \sqrt{L_o^2 * cos^2(\theta) [1 - \frac{v^2 }{c^2} ]+ L_o^2 * sin(\theta)^2}](https://tex.z-dn.net/?f=L_r%20%3D%20%20%5Csqrt%7BL_o%5E2%20%2A%20cos%5E2%28%5Ctheta%29%20%20%5B1%20-%20%5Cfrac%7Bv%5E2%20%7D%7Bc%5E2%7D%20%5D%2B%20L_o%5E2%20%2A%20sin%28%5Ctheta%29%5E2%7D)
=> ![L_r = \sqrt{ [cos^2\theta +sin^2\theta ]- \frac{v^2 }{c^2}cos^2 \theta }](https://tex.z-dn.net/?f=L_r%20%20%3D%20%20%5Csqrt%7B%20%5Bcos%5E2%5Ctheta%20%2Bsin%5E2%5Ctheta%20%5D-%20%5Cfrac%7Bv%5E2%20%7D%7Bc%5E2%7Dcos%5E2%20%5Ctheta%20%7D)
=> ![L_o \sqrt{1 - \frac{v^2}{c^2 } cos^2(\theta ) }](https://tex.z-dn.net/?f=L_o%20%5Csqrt%7B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%20%7D%20cos%5E2%28%5Ctheta%20%29%20%7D)
Hence the length of the rod as measured by a stationary observer is
![L_r = L_o \sqrt{1 - \frac{v^2}{c^2 } cos^2(\theta ) }](https://tex.z-dn.net/?f=%20L_r%20%3D%20L_o%20%5Csqrt%7B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%20%7D%20cos%5E2%28%5Ctheta%20%29%20%7D)
Generally the angle made is mathematically represented
![tan(\theta) = \frac{L_y}{L_x}](https://tex.z-dn.net/?f=tan%28%5Ctheta%29%20%3D%20%20%5Cfrac%7BL_y%7D%7BL_x%7D)
=> ![tan {\theta } = \frac{L_o sin(\theta )}{ (L_o cos(\theta ))\sqrt{ 1 -\frac{v^2}{c^2} } }](https://tex.z-dn.net/?f=tan%20%7B%5Ctheta%20%7D%20%3D%20%20%5Cfrac%7BL_o%20sin%28%5Ctheta%20%29%7D%7B%20%28L_o%20cos%28%5Ctheta%20%29%29%5Csqrt%7B%201%20-%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D%20%7D)
=>
Explanation:
Answer: 3 radians/meter.
Explanation:
The general sinusoidal function will be something like:
y = A*sin(k*x - ω*t) + C
Where:
A is the amplitude.
k is the wave number.
x is the spatial variable
ω is the angular frequency
t is the time variable.
C is the mid-value.
The rule that we can use to solve this problem, is that the argument of the sin( ) function must be in radians (or in degrees)
Then if x is in meters, the wave-number must be in radians/meters, so when these numbers multiply the "meters" part is canceled.
Then for the case of the function:
y(x,t) = 0.1 sin(3x + 10t)
Where x is in meters, the units of the wave number (the 3) must be in radians/meters. Then the angular wave number is 3 radians/meter.