Answer:
Distance = 3.69 × 10^9 m
The distance from the probe to Earth is 3.69 × 10^9 m
Explanation:
Distance from the probe to the Earth can be derived using the simple motion formula;
Distance = speed × time .....1
Since a radio signal uses an electromagnetic wave to transfer signal, it has the same speed as the speed of light.
Speed of radio signal = speed of light = 3.0 × 10^8 m/s
time taken to reach the earth = 12.3 seconds
Substituting the values of speed and time into equation 1;
Distance = 3.0 × 10^8 m/s × 12.3 s
Distance = 36.9 × 10^8 m
Distance = 3.69 × 10^9 m
Note: all electromagnetic radiation have the same speed which is equal to 3.0 × 10^8 m/s
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Answer:
I just took the quiz and got 100% when choosing A.Conservation. Hope this helps:)
The statement that is true of cooling down after physical activity is that you should cool down for about 5 to 10 minutes after being physically active.
With acceleration
![\mathbf a=\left(2.00\dfrac{\rm m}{\mathrm s^2}\right)\,\mathbf j](https://tex.z-dn.net/?f=%5Cmathbf%20a%3D%5Cleft%282.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29%5C%2C%5Cmathbf%20j)
and initial velocity
![\mathbf v(0)=\left(8.00\dfrac{\rm m}{\rm s}\right)\,\mathbf i](https://tex.z-dn.net/?f=%5Cmathbf%20v%280%29%3D%5Cleft%288.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5C%2C%5Cmathbf%20i)
the velocity at time <em>t</em> (b) is given by
![\mathbf v(t)=\mathbf v(0)+\displaystyle\int_0^t\mathbf a\,\mathrm du](https://tex.z-dn.net/?f=%5Cmathbf%20v%28t%29%3D%5Cmathbf%20v%280%29%2B%5Cdisplaystyle%5Cint_0%5Et%5Cmathbf%20a%5C%2C%5Cmathrm%20du)
![\mathbf v(t)=\left(8.00\dfrac{\rm m}{\rm s}\right)\,\mathbf i+\displaystyle\int_0^t\left(2.00\dfrac{\rm m}{\mathrm s^2}\right)\,\mathbf j\,\mathrm du](https://tex.z-dn.net/?f=%5Cmathbf%20v%28t%29%3D%5Cleft%288.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5C%2C%5Cmathbf%20i%2B%5Cdisplaystyle%5Cint_0%5Et%5Cleft%282.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29%5C%2C%5Cmathbf%20j%5C%2C%5Cmathrm%20du)
![\mathbf v(t)=\left(8.00\dfrac{\rm m}{\rm s}\right)\,\mathbf i+\left(2.00\dfrac{\rm m}{\mathrm s^2}\right)u\,\mathbf j\bigg|_{u=0}^{u=t}](https://tex.z-dn.net/?f=%5Cmathbf%20v%28t%29%3D%5Cleft%288.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5C%2C%5Cmathbf%20i%2B%5Cleft%282.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29u%5C%2C%5Cmathbf%20j%5Cbigg%7C_%7Bu%3D0%7D%5E%7Bu%3Dt%7D)
![\mathbf v(t)=\left(8.00\dfrac{\rm m}{\rm s}\right)\,\mathbf i+\left(2.00\dfrac{\rm m}{\mathrm s^2}\right)t\,\mathbf j](https://tex.z-dn.net/?f=%5Cmathbf%20v%28t%29%3D%5Cleft%288.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5C%2C%5Cmathbf%20i%2B%5Cleft%282.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29t%5C%2C%5Cmathbf%20j)
We can get the position at time <em>t</em> (a) by integrating the velocity:
![\mathbf x(t)=\mathbf x(0)+\displaystyle\int_0^t\mathbf v(u)\,\mathrm du](https://tex.z-dn.net/?f=%5Cmathbf%20x%28t%29%3D%5Cmathbf%20x%280%29%2B%5Cdisplaystyle%5Cint_0%5Et%5Cmathbf%20v%28u%29%5C%2C%5Cmathrm%20du)
The particle starts at the origin, so
.
![\mathbf x(t)=\displaystyle\int_0^t\left(8.00\dfrac{\rm m}{\rm s}\right)\,\mathbf i+\left(2.00\dfrac{\rm m}{\mathrm s^2}\right)u\,\mathbf j\,\mathrm du](https://tex.z-dn.net/?f=%5Cmathbf%20x%28t%29%3D%5Cdisplaystyle%5Cint_0%5Et%5Cleft%288.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5C%2C%5Cmathbf%20i%2B%5Cleft%282.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29u%5C%2C%5Cmathbf%20j%5C%2C%5Cmathrm%20du)
![\mathbf x(t)=\left(\left(8.00\dfrac{\rm m}{\rm s}\right)u\,\mathbf i+\dfrac12\left(2.00\dfrac{\rm m}{\mathrm s^2}\right)u^2\,\mathbf j\right)\bigg|_{u=0}^{u=t}](https://tex.z-dn.net/?f=%5Cmathbf%20x%28t%29%3D%5Cleft%28%5Cleft%288.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29u%5C%2C%5Cmathbf%20i%2B%5Cdfrac12%5Cleft%282.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29u%5E2%5C%2C%5Cmathbf%20j%5Cright%29%5Cbigg%7C_%7Bu%3D0%7D%5E%7Bu%3Dt%7D)
![\mathbf x(t)=\left(8.00\dfrac{\rm m}{\rm s}\right)t\,\mathbf i+\left(1.00\dfrac{\rm m}{\mathrm s^2}\right)t^2\,\mathbf j](https://tex.z-dn.net/?f=%5Cmathbf%20x%28t%29%3D%5Cleft%288.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29t%5C%2C%5Cmathbf%20i%2B%5Cleft%281.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29t%5E2%5C%2C%5Cmathbf%20j)
Get the coordinates at <em>t</em> = 8.00 s by evaluating
at this time:
![\mathbf x(8.00\,\mathrm s)=\left(8.00\dfrac{\rm m}{\rm s}\right)(8.00\,\mathrm s)\,\mathbf i+\left(1.00\dfrac{\rm m}{\mathrm s^2}\right)(8.00\,\mathrm s)^2\,\mathbf j](https://tex.z-dn.net/?f=%5Cmathbf%20x%288.00%5C%2C%5Cmathrm%20s%29%3D%5Cleft%288.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%288.00%5C%2C%5Cmathrm%20s%29%5C%2C%5Cmathbf%20i%2B%5Cleft%281.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29%288.00%5C%2C%5Cmathrm%20s%29%5E2%5C%2C%5Cmathbf%20j)
![\mathbf x(8.00\,\mathrm s)=(64.0\,\mathrm m)\,\mathbf i+(64.0\,\mathrm m)\,\mathbf j](https://tex.z-dn.net/?f=%5Cmathbf%20x%288.00%5C%2C%5Cmathrm%20s%29%3D%2864.0%5C%2C%5Cmathrm%20m%29%5C%2C%5Cmathbf%20i%2B%2864.0%5C%2C%5Cmathrm%20m%29%5C%2C%5Cmathbf%20j)
so the particle is located at (<em>x</em>, <em>y</em>) = (64.0, 64.0).
Get the speed at <em>t</em> = 8.00 s by evaluating
at the same time:
![\mathbf v(8.00\,\mathrm s)=\left(8.00\dfrac{\rm m}{\rm s}\right)\,\mathbf i+\left(2.00\dfrac{\rm m}{\mathrm s^2}\right)(8.00\,\mathrm s)\,\mathbf j](https://tex.z-dn.net/?f=%5Cmathbf%20v%288.00%5C%2C%5Cmathrm%20s%29%3D%5Cleft%288.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5C%2C%5Cmathbf%20i%2B%5Cleft%282.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29%288.00%5C%2C%5Cmathrm%20s%29%5C%2C%5Cmathbf%20j)
![\mathbf v(8.00\,\mathrm s)=\left(8.00\dfrac{\rm m}{\rm s}\right)\,\mathbf i+\left(16.0\dfrac{\rm m}{\rm s}\right)\,\mathbf j](https://tex.z-dn.net/?f=%5Cmathbf%20v%288.00%5C%2C%5Cmathrm%20s%29%3D%5Cleft%288.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5C%2C%5Cmathbf%20i%2B%5Cleft%2816.0%5Cdfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5C%2C%5Cmathbf%20j)
This is the <em>velocity</em> at <em>t</em> = 8.00 s. Get the <em>speed</em> by computing the magnitude of this vector:
![\|\mathbf v(8.00\,\mathrm s)\|=\sqrt{\left(8.00\dfrac{\rm m}{\rm s}\right)^2+\left(16.0\dfrac{\rm m}{\rm s}\right)^2}=8\sqrt5\dfrac{\rm m}{\rm s}\approx17.9\dfrac{\rm m}{\rm s}](https://tex.z-dn.net/?f=%5C%7C%5Cmathbf%20v%288.00%5C%2C%5Cmathrm%20s%29%5C%7C%3D%5Csqrt%7B%5Cleft%288.00%5Cdfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5E2%2B%5Cleft%2816.0%5Cdfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5E2%7D%3D8%5Csqrt5%5Cdfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Capprox17.9%5Cdfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D)