Answer:
![m=\frac{m_{0}}{e}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7Bm_%7B0%7D%7D%7Be%7D)
Explanation:
Equation of the rocket is,
![m\frac{dv}{dt} =F-v'\frac{dm}{dt}](https://tex.z-dn.net/?f=m%5Cfrac%7Bdv%7D%7Bdt%7D%20%3DF-v%27%5Cfrac%7Bdm%7D%7Bdt%7D)
Here, v' is the relative velocity of rocket.
In space F is zero.
So,
![m\frac{dv}{dt} =-v'\frac{dm}{dt}\\dv=-v'\frac{dm}{m} \\v=-v'ln\frac{m}{m_{0} }](https://tex.z-dn.net/?f=m%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D-v%27%5Cfrac%7Bdm%7D%7Bdt%7D%5C%5Cdv%3D-v%27%5Cfrac%7Bdm%7D%7Bm%7D%20%5C%5Cv%3D-v%27ln%5Cfrac%7Bm%7D%7Bm_%7B0%7D%20%7D)
Now the momentum can be obtained by multiply by m on both sides.
![P=-v'mln\frac{m}{m_{0} }](https://tex.z-dn.net/?f=P%3D-v%27mln%5Cfrac%7Bm%7D%7Bm_%7B0%7D%20%7D)
Now for maxima, ![\frac{dP}{dm}=0](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdm%7D%3D0)
![-v'ln\frac{m}{m_{0} }-v'm\frac{m_{0}}{m }m_{0=0](https://tex.z-dn.net/?f=-v%27ln%5Cfrac%7Bm%7D%7Bm_%7B0%7D%20%7D-v%27m%5Cfrac%7Bm_%7B0%7D%7D%7Bm%20%7Dm_%7B0%3D0)
Now,
![ln(\frac{m}{m_{0} } )=-1\\\frac{m}{m_{0} }=\frac{1}{e} \\m=\frac{m_{0}}{e}](https://tex.z-dn.net/?f=ln%28%5Cfrac%7Bm%7D%7Bm_%7B0%7D%20%7D%20%29%3D-1%5C%5C%5Cfrac%7Bm%7D%7Bm_%7B0%7D%20%7D%3D%5Cfrac%7B1%7D%7Be%7D%20%5C%5Cm%3D%5Cfrac%7Bm_%7B0%7D%7D%7Be%7D)
Therefore, the mass of the rocket while having maximum momentum is ![\frac{m_{0}}{e}](https://tex.z-dn.net/?f=%5Cfrac%7Bm_%7B0%7D%7D%7Be%7D)
Answer:
B
Explanation:
B is the most likely region that contains alkaline earth family elements.
The correct answer is inertia
Answer:
.25 m/s
Explanation:
We shall use the law of conservation of momentum . We do not use law of conservation of mechanical energy because in such cases there is loss of energy.
Momentum = mass x velocity
Initial momentum of arrow and block
= .15 x 30 +0 = 4.5 J
If final velocity of block be V
Total final momentum of both arrow and block
= .15 x 25 + 3 V
= 3.75 +3V
So
3.75 + 3 V = 4.5
V = .25 m/s
The work W done on an object by a constant force is defined as W = F. d. It is equal to the magnitude of the force, multiplied by the distance the object moves in the direction of the force.