Answer:
52.49 Kg
Explanation:
Let m1 and v1 denote your mass and velocity respectively
Let m2 and v2 denote your friends mass and velocity respectively
Kinetic energy is given by
Since your kinetic energies are the same hence
and making m2 the subject then
Since v2 is v1+0.28v1=1.28v1
Substituting m1 for 86 Kg
To solve this problem it is necessary to apply the concepts related to gravity as an expression of a celestial body, as well as the use of concepts such as centripetal acceleration, angular velocity and period.
PART A) The expression to find the acceleration of the earth due to the gravity of another celestial body as the Moon is given by the equation
![g = \frac{GM}{(d-R_{CM})^2}](https://tex.z-dn.net/?f=g%20%3D%20%5Cfrac%7BGM%7D%7B%28d-R_%7BCM%7D%29%5E2%7D)
Where,
G = Gravitational Universal Constant
d = Distance
M = Mass
Radius earth center of mass
PART B) Using the same expression previously defined we can find the acceleration of the moon on the earth like this,
![g = \frac{GM}{(d-R_{CM})^2}](https://tex.z-dn.net/?f=g%20%3D%20%5Cfrac%7BGM%7D%7B%28d-R_%7BCM%7D%29%5E2%7D)
![g = \frac{(6.67*10^{-11})(7.35*10^{22})}{(3.84*10^8-4700*10^3)^2}](https://tex.z-dn.net/?f=g%20%3D%20%5Cfrac%7B%286.67%2A10%5E%7B-11%7D%29%287.35%2A10%5E%7B22%7D%29%7D%7B%283.84%2A10%5E8-4700%2A10%5E3%29%5E2%7D)
![g = 3.4*10^{-5}m/s^2](https://tex.z-dn.net/?f=g%20%3D%203.4%2A10%5E%7B-5%7Dm%2Fs%5E2)
PART C) Centripetal acceleration can be found throughout the period and angular velocity, that is
![\omega = \frac{2\pi}{T}](https://tex.z-dn.net/?f=%5Comega%20%3D%20%5Cfrac%7B2%5Cpi%7D%7BT%7D)
At the same time we have that centripetal acceleration is given as
![a_c = \omega^2 r](https://tex.z-dn.net/?f=a_c%20%3D%20%5Comega%5E2%20r)
Replacing
![a_c = (\frac{2\pi}{T})^2 r](https://tex.z-dn.net/?f=a_c%20%3D%20%28%5Cfrac%7B2%5Cpi%7D%7BT%7D%29%5E2%20r)
![a_c = (\frac{2\pi}{26.3d(\frac{86400s}{1days})})^2 (4700*10^3m)](https://tex.z-dn.net/?f=a_c%20%3D%20%28%5Cfrac%7B2%5Cpi%7D%7B26.3d%28%5Cfrac%7B86400s%7D%7B1days%7D%29%7D%29%5E2%20%284700%2A10%5E3m%29)
![a_c = 3.34*10^{-5}m/s^2](https://tex.z-dn.net/?f=a_c%20%3D%203.34%2A10%5E%7B-5%7Dm%2Fs%5E2)
Missing figure: http://d2vlcm61l7u1fs.cloudfront.net/media/f5d/f5d9d0bc-e05f-4cd8-9277-da7cdda3aebf/phpJK1JgJ.png
Solution:
We need to find the magnitude of the resultant on both x- and y-axis.
x-axis) The resultant on the x-axis is
![F_x = 65 N\cdot cos 30^{\circ} - 30 N - 20 N\cdot sin 20^{\circ} = 19.45 N](https://tex.z-dn.net/?f=F_x%20%3D%2065%20N%5Ccdot%20cos%2030%5E%7B%5Ccirc%7D%20-%2030%20N%20-%2020%20N%5Ccdot%20sin%2020%5E%7B%5Ccirc%7D%20%3D%2019.45%20N)
in the positive direction.
y-axis) The resultant on the y-axis is
![F_y = 65 N \cdot sin 30^{\circ} - 20 N \cdot cos 20^{\circ} = 13.70 N](https://tex.z-dn.net/?f=F_y%20%3D%2065%20N%20%5Ccdot%20sin%2030%5E%7B%5Ccirc%7D%20-%2020%20N%20%5Ccdot%20cos%2020%5E%7B%5Ccirc%7D%20%3D%2013.70%20N)
in the positive direction.
Both Fx and Fy are positive, so the resultant is in the first quadrant. We can find the angle and so the direction using
![\tan \alpha = \frac{F_y}{F_x} = \frac{13.70 N}{19.45 N}=0.7](https://tex.z-dn.net/?f=%5Ctan%20%5Calpha%20%3D%20%20%5Cfrac%7BF_y%7D%7BF_x%7D%20%3D%20%5Cfrac%7B13.70%20N%7D%7B19.45%20N%7D%3D0.7%20)
from which we find
Because they behave just like all the electromagnetic waves of the spectrum. Same equations, just shorter wavelengths and more energy.
Hope you get it :)
To determine the diameter of the earth in metres first multiply the original value by 2.
6378 X 2 = 12 756 km.
Then convert km - m
1 km = 1000 m
12 756 km = ? m
12 756 • 1000 = 12 756 000 = 12 756 000 m or 1.2756 X 10 ^ 7 m
The final solution for the diameter is 1.2756 X 10 ^ 7 m.