The rocket engine works on the basic principle proposed by Newton which is Newton’s Third Law.
-- The table tennis ball bounces back with virtually its entire original speed.
-- The bowling ball rolls forward, so slowly that only complex expensive laboratory equipment can detect and measure its speed.
-- Once again, momentum is conserved !
Answer:
![x = t](https://tex.z-dn.net/?f=x%20%3D%20t)
![y = \frac{1}{3}t](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B3%7Dt)
![z =t](https://tex.z-dn.net/?f=z%20%3Dt)
Explanation:
Given
at ![t = 0](https://tex.z-dn.net/?f=t%20%3D%200)
Point: ![(f(t0), g(t0), h(t0))](https://tex.z-dn.net/?f=%28f%28t0%29%2C%20g%28t0%29%2C%20h%28t0%29%29)
,
-- Missing Information
Required
Determine the parametric equations
![r(t) = ln\ ti + \frac{t-1}{t+2}j + t\ ln\ tk](https://tex.z-dn.net/?f=r%28t%29%20%3D%20ln%5C%20ti%20%2B%20%5Cfrac%7Bt-1%7D%7Bt%2B2%7Dj%20%2B%20t%5C%20ln%5C%20tk)
Differentiate with respect to t
![r'(t) = \frac{1}{t}i +\frac{3}{(t+2)^2}j + (ln\ t + 1)k](https://tex.z-dn.net/?f=r%27%28t%29%20%3D%20%5Cfrac%7B1%7D%7Bt%7Di%20%2B%5Cfrac%7B3%7D%7B%28t%2B2%29%5E2%7Dj%20%2B%20%28ln%5C%20t%20%2B%201%29k)
Let t = 1 (i.e
)
![r'(1) = \frac{1}{1}i +\frac{3}{(1+2)^2}j + (ln\ 1 + 1)k](https://tex.z-dn.net/?f=r%27%281%29%20%3D%20%5Cfrac%7B1%7D%7B1%7Di%20%2B%5Cfrac%7B3%7D%7B%281%2B2%29%5E2%7Dj%20%2B%20%28ln%5C%201%20%2B%201%29k)
![r'(1) = i +\frac{3}{3^2}j + (0 + 1)k](https://tex.z-dn.net/?f=r%27%281%29%20%3D%20i%20%2B%5Cfrac%7B3%7D%7B3%5E2%7Dj%20%2B%20%280%20%2B%201%29k)
![r'(1) = i +\frac{3}{9}j + (1)k](https://tex.z-dn.net/?f=r%27%281%29%20%3D%20i%20%2B%5Cfrac%7B3%7D%7B9%7Dj%20%2B%20%281%29k)
![r'(1) = i +\frac{1}{3}j + (1)k](https://tex.z-dn.net/?f=r%27%281%29%20%3D%20i%20%2B%5Cfrac%7B1%7D%7B3%7Dj%20%2B%20%281%29k)
![r'(1) = i +\frac{1}{3}j + k](https://tex.z-dn.net/?f=r%27%281%29%20%3D%20i%20%2B%5Cfrac%7B1%7D%7B3%7Dj%20%2B%20k)
To solve for x, y and z, we make use of:
![r(t) = f(t)i + g(t)j + h(t)k](https://tex.z-dn.net/?f=r%28t%29%20%3D%20f%28t%29i%20%2B%20g%28t%29j%20%2B%20h%28t%29k)
This implies that:
![r'(1)t = xi + yj + zk](https://tex.z-dn.net/?f=r%27%281%29t%20%3D%20xi%20%2B%20yj%20%2B%20zk)
So, we have:
![xi + yj + zk = (i +\frac{1}{3}j + k)t](https://tex.z-dn.net/?f=xi%20%2B%20yj%20%2B%20zk%20%20%3D%20%28i%20%2B%5Cfrac%7B1%7D%7B3%7Dj%20%2B%20k%29t)
![xi + yj + zk = it +\frac{1}{3}jt + kt](https://tex.z-dn.net/?f=xi%20%2B%20yj%20%2B%20zk%20%20%3D%20it%20%2B%5Cfrac%7B1%7D%7B3%7Djt%20%2B%20kt)
By comparison:
![xi = it](https://tex.z-dn.net/?f=xi%20%3D%20it)
Divide by i
![x = t](https://tex.z-dn.net/?f=x%20%3D%20t)
Divide by j
![y = \frac{1}{3}t](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B3%7Dt)
![zk = kt](https://tex.z-dn.net/?f=zk%20%3D%20kt)
Divide by k
![z = t](https://tex.z-dn.net/?f=z%20%3D%20t)
Hence, the parametric equations are:
![x = t](https://tex.z-dn.net/?f=x%20%3D%20t)
![y = \frac{1}{3}t](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B3%7Dt)
![z =t](https://tex.z-dn.net/?f=z%20%3Dt)
Answer:
Doppler effect changes the wavelength of the light emitted, depending upon whether source is moving away or coming towards the observer(detector).
Explanation:
Doppler effect in light is actually a relativistic effect but somewhat similar to the one which happens in sound waves.
When the source is moving away from the detector, the wavelength of the light emitted from the source appears to be increased as seen by the detector, as a result the frequency decreases(we know that frequency of light= speed of light/wavelength of light. Here speed of light is constant and frequency of light is inversely proportional to its wavelength)
Due to this decrease in frequency the light emitted from the source appears more red, since red color is on low frequency side in the electromagnetic spectrum.
Similarly for the source moving towards the detector, the wavelength appears to be decreased, thereby resulting in increase in frequency and the source appears blue. The shift in frequency is known as doppler shift.
The shift in frequency when the source is moving away is known as redshift and the one where the source is moving towards detector is known as blueshift
That depends on which angle you picked first, because that determines
which angles "the other two" are.
If you picked the right angle (90°) first, before you asked the question,
then the other two are acute angles, and they're also complementary