Answer:
Average speed = 1.2 m/s
Average velocity = 0.4 m/s
Explanation:
Average speed = total distance/total time
Average speed = (40 + 20)/(40 + 10)
Average speed = 60/50
Average speed = 1.2 m/s
Average velocity = displacement/time
Now, she ran 40 m south and ran 20 m back north which is in the direction of where she began the journey.
Thus;
Displacement = 40 - 20 = 20 m
Average velocity = 20/50 = 0.4 m/s
Answer:
F=8.0*10^{-10}N
Explanation:
See the attached file for the masses distributions
The force between two masses at distance r is expressed as

since the masses are of the same value, the above formula can be reduce to

using vector notation,Let use consider the force on the lower left corner of the mass due to the upper left side of the mass is

The force on the lower left corner of the mass due to the lower right side of the mass is

The force on the lower left corner of the mass due to the upper right side of the mass is

The net force can be express as
![F=\frac{Gm^{2}}{r^{2} }j +\frac{Gm^{2}}{r^{2} }i +\frac{Gm^{2}}{d^{2} }cos\alpha i +\frac{Gm^{2}}{d^{2} }sin\alpha j\\\\F=Gm^{2}[\frac{1}{r^{2}}+ \frac{1}{d^{2}cos\alpha }]i + Gm^{2}[\frac{1}{r^{2}}+ \frac{1}{d^{2}sin\alpha }]j\\\alpha=45^{0}, G=6.67*10^{-11}Nmkg^{-2}](https://tex.z-dn.net/?f=F%3D%5Cfrac%7BGm%5E%7B2%7D%7D%7Br%5E%7B2%7D%20%7Dj%20%2B%5Cfrac%7BGm%5E%7B2%7D%7D%7Br%5E%7B2%7D%20%7Di%20%2B%5Cfrac%7BGm%5E%7B2%7D%7D%7Bd%5E%7B2%7D%20%7Dcos%5Calpha%20i%20%2B%5Cfrac%7BGm%5E%7B2%7D%7D%7Bd%5E%7B2%7D%20%7Dsin%5Calpha%20j%5C%5C%5C%5CF%3DGm%5E%7B2%7D%5B%5Cfrac%7B1%7D%7Br%5E%7B2%7D%7D%2B%20%5Cfrac%7B1%7D%7Bd%5E%7B2%7Dcos%5Calpha%20%7D%5Di%20%2B%20Gm%5E%7B2%7D%5B%5Cfrac%7B1%7D%7Br%5E%7B2%7D%7D%2B%20%5Cfrac%7B1%7D%7Bd%5E%7B2%7Dsin%5Calpha%20%7D%5Dj%5C%5C%5Calpha%3D45%5E%7B0%7D%2C%20G%3D6.67%2A10%5E%7B-11%7DNmkg%5E%7B-2%7D)
if we insert values we arrive at
![F=6.67*10^{-11}*2.5^{2}[\frac{1}{1^{2}}+ \frac{1}{\sqrt{2}^{2}cos45 }]i + 6.67*10^{-11}*2.5^{2}[\frac{1}{1^{2}}+ \frac{1}{\sqrt{2}^{2}sin45}]j\\F=5.643*10^{-10}i+5.643*10^{-10}j](https://tex.z-dn.net/?f=F%3D6.67%2A10%5E%7B-11%7D%2A2.5%5E%7B2%7D%5B%5Cfrac%7B1%7D%7B1%5E%7B2%7D%7D%2B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%5E%7B2%7Dcos45%20%7D%5Di%20%2B%206.67%2A10%5E%7B-11%7D%2A2.5%5E%7B2%7D%5B%5Cfrac%7B1%7D%7B1%5E%7B2%7D%7D%2B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%5E%7B2%7Dsin45%7D%5Dj%5C%5CF%3D5.643%2A10%5E%7B-10%7Di%2B5.643%2A10%5E%7B-10%7Dj)
if we solve for the magnitude, we arrive at

Hence the net force on one of the masses is

Answer:
v = 7.9 m/s
Explanation:
length of the vine (L) = 20 m
initial angle with the vertical = 45 degrees
final angle with the vertical = 30 degrees
acceleration due to gravity (g) = 9.8 m/s^{2}
speed (v) =?
to solve this problem we can apply the equation below:
loss in potential energy = gain in kinetic energy
m x g x h = 1/2 x m x 
v = 
before we can apply the above we need to get our height
height = initial vertical height - final vertical height
height = (L - L cosθ2) - (L - L cosθ1)
height = (20 - 20cos45) - (20 - 20cos30) = 3.2 m
v = 
v = 7.9 m/s