Explanation:
Using Newtons second law on each block
F = m*a
Block 1
![T_{1} - u*g*M_{1} = M_{1} *a \\\\T_{1} = M_{1}*(a + u*g) ... Eq1](https://tex.z-dn.net/?f=T_%7B1%7D%20-%20u%2Ag%2AM_%7B1%7D%20%3D%20M_%7B1%7D%20%2Aa%20%5C%5C%5C%5CT_%7B1%7D%20%3D%20M_%7B1%7D%2A%28a%20%2B%20u%2Ag%29%20...%20Eq1)
Block 2
![T_{2} - u*g*M_{2} = M_{2} *a \\\\T_{2} = M_{2}*(a + u*g) ... Eq2](https://tex.z-dn.net/?f=T_%7B2%7D%20-%20u%2Ag%2AM_%7B2%7D%20%3D%20M_%7B2%7D%20%2Aa%20%5C%5C%5C%5CT_%7B2%7D%20%3D%20M_%7B2%7D%2A%28a%20%2B%20u%2Ag%29%20...%20Eq2)
Block 3
![- (T_{1} + T_{2} ) + g*M_{3} = M_{3} *a \\\\T_{1} + T_{2} = M_{3}*( -a + g) ... Eq3](https://tex.z-dn.net/?f=-%20%28T_%7B1%7D%20%2B%20T_%7B2%7D%20%29%20%2B%20g%2AM_%7B3%7D%20%3D%20M_%7B3%7D%20%2Aa%20%5C%5C%5C%5CT_%7B1%7D%20%2B%20T_%7B2%7D%20%3D%20M_%7B3%7D%2A%28%20-a%20%2B%20g%29%20...%20Eq3)
Solving Eq1,2,3 simultaneously
Divide 1 and 2
![\frac{T_{1} }{T_{2}} = \frac{M_{1}*(a+u*g)}{M_{2}*(a+u*g)} \\\\\frac{T_{1} }{T_{2}} = \frac{M_{1} }{M_{2} }\\\\ T_{1} = \frac{M_{1} *T_{2} }{M_{2} } .... Eq4](https://tex.z-dn.net/?f=%5Cfrac%7BT_%7B1%7D%20%7D%7BT_%7B2%7D%7D%20%3D%20%5Cfrac%7BM_%7B1%7D%2A%28a%2Bu%2Ag%29%7D%7BM_%7B2%7D%2A%28a%2Bu%2Ag%29%7D%20%20%5C%5C%5C%5C%5Cfrac%7BT_%7B1%7D%20%7D%7BT_%7B2%7D%7D%20%3D%20%5Cfrac%7BM_%7B1%7D%20%7D%7BM_%7B2%7D%20%7D%5C%5C%5C%5C%20T_%7B1%7D%20%3D%20%20%5Cfrac%7BM_%7B1%7D%20%2AT_%7B2%7D%20%7D%7BM_%7B2%7D%20%7D%20....%20Eq4)
Put Eq 4 into Eq3
![T_{2} = \frac{M_{3}*(g-a) }{1+\frac{M_{1} }{M_{2} } } ...Eq5](https://tex.z-dn.net/?f=T_%7B2%7D%20%3D%20%5Cfrac%7BM_%7B3%7D%2A%28g-a%29%20%7D%7B1%2B%5Cfrac%7BM_%7B1%7D%20%7D%7BM_%7B2%7D%20%7D%20%7D%20%20...Eq5)
Put Eq 5 into Eq2 and solve for a
![a = \frac{M_{3}*g -u*g*(M_{1} + M_{2}) }{M_{1} + M_{2} + M_{3} } .... Eq6](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7BM_%7B3%7D%2Ag%20-u%2Ag%2A%28M_%7B1%7D%20%2B%20M_%7B2%7D%29%20%7D%7BM_%7B1%7D%20%2B%20M_%7B2%7D%20%2B%20M_%7B3%7D%20%7D%20%20....%20Eq6)
Substitute back in Eq2 and use Eq4 and solve for T2 & T1
![T_{2} = M_{2}*M_{3}*g*(\frac{1-u}{M_{1} + M_{2}+M_{3}})\\\\T_{1} = M_{1}*M_{3}*g*(\frac{1-u}{M_{1} + M_{2}+M_{3}})\\\\](https://tex.z-dn.net/?f=T_%7B2%7D%20%3D%20M_%7B2%7D%2AM_%7B3%7D%2Ag%2A%28%5Cfrac%7B1-u%7D%7BM_%7B1%7D%20%2B%20M_%7B2%7D%2BM_%7B3%7D%7D%29%5C%5C%5C%5CT_%7B1%7D%20%3D%20M_%7B1%7D%2AM_%7B3%7D%2Ag%2A%28%5Cfrac%7B1-u%7D%7BM_%7B1%7D%20%2B%20M_%7B2%7D%2BM_%7B3%7D%7D%29%5C%5C%5C%5C)
Answer:
C) Venus is closer to the Sun than Saturn is.
Explanation:
This is the right answer.
Answer:
77.9 km/h
Explanation:
We determine the initial momenta of lion and gazelle.
Lion: 173 × 80.9 = 13995.7
Gazelle: 36.2 × 63.8 = 2309.56
Since they are running in the same direction, we add their momenta to get the total initial momentum:
![p_1 = 13995.7+2309.56 = 16305.26](https://tex.z-dn.net/?f=p_1%20%3D%2013995.7%2B2309.56%20%3D%2016305.26)
After the collision, they are together and have a common velocity. Hence, the total final momentum is
![p_2 = (173+36.2)\times v = 209.2v](https://tex.z-dn.net/?f=p_2%20%3D%20%28173%2B36.2%29%5Ctimes%20v%20%3D%20209.2v)
By the principle of conservation of momentum, the total initial momentum is equal to the total final momentum, provided there are no external forces.
![209.2v = 16305.26](https://tex.z-dn.net/?f=209.2v%20%3D%2016305.26)
![v = \dfrac{16305.26}{209.2} = 77.9 \text{ km/h}](https://tex.z-dn.net/?f=v%20%3D%20%5Cdfrac%7B16305.26%7D%7B209.2%7D%20%3D%2077.9%20%5Ctext%7B%20km%2Fh%7D)
Answer: Generally, prevailing winds blow east-west rather than north-south. This happens because Earth's rotation generates what is known as the Coriolis effect. The Coriolis effect makes wind systems twist counter-clockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere.
Explanation: here u go