Answer:
![v_{s}=65.2km/h](https://tex.z-dn.net/?f=v_%7Bs%7D%3D65.2km%2Fh)
Explanation:
Given data
Flight distance S=4890 km
Time difference Δt=t₂-t₁=40 min
Air speed of plane=980 km/h
To find
Speed of jet stream
Solution
When moving in the same direction as the jet stream time taken as t₁=d/(v+vs),v is velocity of plane and vs is velocity of plane
While moving in opposite direction t₂=d/(v+vs)
So
![t_{2}-t_{1}=\frac{d}{(v-v_{s}) } - \frac{d}{(v+v_{s}) }\\t_{2}-t_{1}=\frac{d(v+v_{s})-d(v-v_{s})}{(v-v_{s})(v+v_{s})} \\t_{2}-t_{1}=\frac{2dv_{s}}{(v)^{2} -(v_{s})^{2} }\\0.666667h=\frac{2(4890km)v_{s}}{(980km/h)^{2} -(v_{s})^{2} }\\0.666667((980km/h)^{2} -(v_{s})^{2})=9780v_{s}\\640267-0.666667(v_{s})^{2}-9780v_{s}=0\\0.666667(v_{s})^{2}+9780v_{s}-640267=0](https://tex.z-dn.net/?f=t_%7B2%7D-t_%7B1%7D%3D%5Cfrac%7Bd%7D%7B%28v-v_%7Bs%7D%29%20%7D%20-%20%5Cfrac%7Bd%7D%7B%28v%2Bv_%7Bs%7D%29%20%7D%5C%5Ct_%7B2%7D-t_%7B1%7D%3D%5Cfrac%7Bd%28v%2Bv_%7Bs%7D%29-d%28v-v_%7Bs%7D%29%7D%7B%28v-v_%7Bs%7D%29%28v%2Bv_%7Bs%7D%29%7D%20%5C%5Ct_%7B2%7D-t_%7B1%7D%3D%5Cfrac%7B2dv_%7Bs%7D%7D%7B%28v%29%5E%7B2%7D%20-%28v_%7Bs%7D%29%5E%7B2%7D%20%7D%5C%5C0.666667h%3D%5Cfrac%7B2%284890km%29v_%7Bs%7D%7D%7B%28980km%2Fh%29%5E%7B2%7D%20-%28v_%7Bs%7D%29%5E%7B2%7D%20%7D%5C%5C0.666667%28%28980km%2Fh%29%5E%7B2%7D%20-%28v_%7Bs%7D%29%5E%7B2%7D%29%3D9780v_%7Bs%7D%5C%5C640267-0.666667%28v_%7Bs%7D%29%5E%7B2%7D-9780v_%7Bs%7D%3D0%5C%5C0.666667%28v_%7Bs%7D%29%5E%7B2%7D%2B9780v_%7Bs%7D-640267%3D0)
Apply quadratic formula to solve for vs
So
Energy is what makes change happen and can be transferred form one object to another. Energy can also be transformed from one form to another. Power is the rate at which energy is transferred. It is not energy but is often confused with energy.
![\text { The force between the given two objects is } 1.865 \times 10^{-6} \mathrm{N}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20The%20force%20between%20the%20given%20two%20objects%20is%20%7D%201.865%20%5Ctimes%2010%5E%7B-6%7D%20%5Cmathrm%7BN%7D)
<u>Explanation</u>:
As per given question,
![m_{1} \text { is } 140 \mathrm{kg}](https://tex.z-dn.net/?f=m_%7B1%7D%20%5Ctext%20%7B%20is%20%7D%20140%20%5Cmathrm%7Bkg%7D)
![m_{2} \text { is } 160 \mathrm{kg}](https://tex.z-dn.net/?f=m_%7B2%7D%20%5Ctext%20%7B%20is%20%7D%20160%20%5Cmathrm%7Bkg%7D)
R is 0.895 m
The force between two objects is
![\mathrm{F}=\frac{G m_{1} m_{2}}{R^{2}}](https://tex.z-dn.net/?f=%5Cmathrm%7BF%7D%3D%5Cfrac%7BG%20m_%7B1%7D%20m_%7B2%7D%7D%7BR%5E%7B2%7D%7D)
Where,
F is the force of attraction between two objects in Newton’s (N)
![\text { G is the Universal Gravitational Constant }=6.674 \times 10^{-11} \mathrm{N}-\mathrm{m}^{2} / \mathrm{kg}^{2}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20G%20is%20the%20Universal%20Gravitational%20Constant%20%7D%3D6.674%20%5Ctimes%2010%5E%7B-11%7D%20%5Cmathrm%7BN%7D-%5Cmathrm%7Bm%7D%5E%7B2%7D%20%2F%20%5Cmathrm%7Bkg%7D%5E%7B2%7D)
![m_{1} \text { and } m_{2} \text { are the masses of the two objects in kilograms (kg) }](https://tex.z-dn.net/?f=m_%7B1%7D%20%5Ctext%20%7B%20and%20%7D%20m_%7B2%7D%20%5Ctext%20%7B%20are%20the%20masses%20of%20the%20two%20objects%20in%20kilograms%20%28kg%29%20%7D)
R is the separation in meters (m) between the objects
Substitute the given values in the above formula,
![F=\frac{6.674 \times 10^{-11} \times 140 \times 160}{0.895^{2}}](https://tex.z-dn.net/?f=F%3D%5Cfrac%7B6.674%20%5Ctimes%2010%5E%7B-11%7D%20%5Ctimes%20140%20%5Ctimes%20160%7D%7B0.895%5E%7B2%7D%7D)
![F=\frac{1.494 \times 10^{-6}}{0.801}](https://tex.z-dn.net/?f=F%3D%5Cfrac%7B1.494%20%5Ctimes%2010%5E%7B-6%7D%7D%7B0.801%7D)
![\mathrm{F}=1.865 \times 10^{-6}](https://tex.z-dn.net/?f=%5Cmathrm%7BF%7D%3D1.865%20%5Ctimes%2010%5E%7B-6%7D)
![\text { The force between the given two objects is } 1.865 \times 10^{-6} \mathrm{N}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20The%20force%20between%20the%20given%20two%20objects%20is%20%7D%201.865%20%5Ctimes%2010%5E%7B-6%7D%20%5Cmathrm%7BN%7D)
Answer:
Many things, such as building the Great Wall of China, and building highways.
Explanation: