Answer:
Distance = 64 metres
Displacement = 28 metres
Direction = northward
Explanation:
Given that a kayaker moves 22 meters northward, then 18 meters southward , and finally 24 meters northward
Distance covered is only about the magnitude of the length covered.
Distance = 22 + 18 + 24 = 64 metres
The direction will be considered when calculating the displacement
Let northward be positive and southward be negative
Displacement = 22 - 18 + 24 = 28 metres
Since the displacement is positive, the direction of the motion is northward.
Answer:
9.6 km/h
Explanation:
20 minutes=1/3 minute.
The speed of the bicycle: 3.2:1/3=9.6 km/h.
Answer: 9.6 km/h
Answer:
The permittivity of rubber is ![\epsilon = 8.703 *10^{-11}](https://tex.z-dn.net/?f=%5Cepsilon%20%20%3D%208.703%20%2A10%5E%7B-11%7D)
Explanation:
From the question we are told that
The magnitude of the point charge is ![q_1 = 70 \ nC = 70 *10^{-9} \ C](https://tex.z-dn.net/?f=q_1%20%3D%20%2070%20%5C%20nC%20%20%3D%20%2070%20%2A10%5E%7B-9%7D%20%5C%20%20C)
The diameter of the rubber shell is ![d = 32 \ cm = 0.32 \ m](https://tex.z-dn.net/?f=d%20%3D%2032%20%5C%20cm%20%20%3D%20%200.32%20%5C%20m)
The Electric field inside the rubber shell is ![E = 2500 \ N/ C](https://tex.z-dn.net/?f=E%20%3D%20%202500%20%5C%20N%2F%20C)
The radius of the rubber is mathematically evaluated as
![r = \frac{d}{2} = \frac{0.32}{2} = 0.16 \ m](https://tex.z-dn.net/?f=r%20%3D%20%20%5Cfrac%7Bd%7D%7B2%7D%20%3D%20%20%5Cfrac%7B0.32%7D%7B2%7D%20%20%3D%20%200.16%20%5C%20m)
Generally the electric field for a point is in an insulator(rubber) is mathematically represented as
Where
is the permittivity of rubber
=> ![E * \epsilon * 4 * \pi * r^2 = Q](https://tex.z-dn.net/?f=E%20%20%2A%20%20%5Cepsilon%20%20%2A%20%204%20%2A%20%5Cpi%20%2A%20%20r%5E2%20%3D%20%20Q)
=> ![\epsilon = \frac{Q}{E * 4 * \pi * r^2}](https://tex.z-dn.net/?f=%5Cepsilon%20%20%3D%20%20%5Cfrac%7BQ%7D%7BE%20%2A%20%204%20%2A%20%20%5Cpi%20%2A%20%20r%5E2%7D)
substituting values
![\epsilon = \frac{70 *10^{-9}}{2500 * 4 * 3.142 * (0.16)^2}](https://tex.z-dn.net/?f=%5Cepsilon%20%20%3D%20%20%5Cfrac%7B70%20%2A10%5E%7B-9%7D%7D%7B2500%20%2A%20%204%20%2A%20%203.142%20%2A%20%20%280.16%29%5E2%7D)
![\epsilon = 8.703 *10^{-11}](https://tex.z-dn.net/?f=%5Cepsilon%20%20%3D%208.703%20%2A10%5E%7B-11%7D)
Answer:
Number of revolutions=1.532 revolutions
Explanation:
Given data
Distance s=8.0 m
Angular speed a=1.2 rev/s
To find
Number of revolutions
Solution
From the equation of simple motion we not that
![S=ut+1/2gt^{2}\\ where\\u=0\\So\\8.0m=0+(1/2)(9.8m/s^{2} )t^{2}\\ t^{2}=\frac{8.0m}{0.5*9.8m/s^{2} } \\ t^{2}=1.63\\t=\sqrt{1.63} \\t=1.28s](https://tex.z-dn.net/?f=S%3Dut%2B1%2F2gt%5E%7B2%7D%5C%5C%20where%5C%5Cu%3D0%5C%5CSo%5C%5C8.0m%3D0%2B%281%2F2%29%289.8m%2Fs%5E%7B2%7D%20%29t%5E%7B2%7D%5C%5C%20t%5E%7B2%7D%3D%5Cfrac%7B8.0m%7D%7B0.5%2A9.8m%2Fs%5E%7B2%7D%20%7D%20%5C%5C%20t%5E%7B2%7D%3D1.63%5C%5Ct%3D%5Csqrt%7B1.63%7D%20%5C%5Ct%3D1.28s)
So for the number of revolutions she makes is given as
![n=a*t\\n=(1.2rev/s)(1.28s)\\n=1.532revolutions](https://tex.z-dn.net/?f=n%3Da%2At%5C%5Cn%3D%281.2rev%2Fs%29%281.28s%29%5C%5Cn%3D1.532revolutions)