Answer:
The resulting velocity of marble B after the collision is 0.96 m/s.
Explanation:
Mass of marble A ,![m_1= 0.08 kg](https://tex.z-dn.net/?f=m_1%3D%200.08%20kg)
Initial velocity of the marble A,![u_1 = 0.5 m/s](https://tex.z-dn.net/?f=u_1%20%3D%200.5%20m%2Fs)
Mass of marble B,![m_2 = 0.05 kg](https://tex.z-dn.net/?f=m_2%20%3D%200.05%20kg)
Initial velocity of the marble B,![u_2 = 0 m/s](https://tex.z-dn.net/?f=u_2%20%3D%200%20m%2Fs)
final velocity of the marble A,![v_1 = -0.1 m/s](https://tex.z-dn.net/?f=v_1%20%3D%20-0.1%20m%2Fs)
final velocity of the marble B,![v_2 = ?](https://tex.z-dn.net/?f=v_2%20%3D%20%3F)
Applying law of conservation of mass:
![m_1u_1+m_2u_2=m_1v_1+m_2v_2](https://tex.z-dn.net/?f=m_1u_1%2Bm_2u_2%3Dm_1v_1%2Bm_2v_2)
![0.08 kg\times 0.5 m/s+0.05kg\times 0 m/s=0.08 kg\times (-0.1 m/s)+0.05kg \times v_2](https://tex.z-dn.net/?f=0.08%20kg%5Ctimes%200.5%20m%2Fs%2B0.05kg%5Ctimes%200%20m%2Fs%3D0.08%20kg%5Ctimes%20%28-0.1%20m%2Fs%29%2B0.05kg%20%5Ctimes%20v_2)
![v_2=0.96 /s](https://tex.z-dn.net/?f=%20v_2%3D0.96%20%2Fs)
The resulting velocity of marble B after the collision is 0.96 m/s.
<span>The control group is the rose bush. </span>The dependent variable is the variable which can be manipulated and can affect the independent variable. The dependent variable is on the x-axis while the independent variable is placed on the y-axis. The dependent variable is the number of months and the independent variable is the number of flowers in each bush.
Answer:
The first law of thermodynamics doesn't actually specify that matter can neither be created nor destroyed, but instead that the total amount of energy in a closed system cannot be created nor destroyed (though it can be changed from one form to another).
Explanation:
The rocket should be fired for <u>129600 seconds.</u>
Why?
We can calculate for how long should the rocket be fired by using the following equation:
![Force=mass*aacceleration=mass*\frac{v-v_{o}}{time} \\\\time=\frac{mass*(v-v_{o})}{Force}](https://tex.z-dn.net/?f=Force%3Dmass%2Aaacceleration%3Dmass%2A%5Cfrac%7Bv-v_%7Bo%7D%7D%7Btime%7D%20%5C%5C%5C%5Ctime%3D%5Cfrac%7Bmass%2A%28v-v_%7Bo%7D%29%7D%7BForce%7D)
From the statement we know:
- Initial speed equal to zero.
- Force equal to 272N.
- Final speed (for the moment) equal to 62 m/s.
- Mass equal to 72000 Kg.
So, substituting and calculating, we have:
![time=\frac{mass*(v-v_{o})}{Force}](https://tex.z-dn.net/?f=time%3D%5Cfrac%7Bmass%2A%28v-v_%7Bo%7D%29%7D%7BForce%7D)
![time=\frac{mass*(v-v_{o})}{Force}\\\\time=\frac{72000*(63\frac{m}{s} -0)}{35\frac{Kg.m}{s^{2}}}=129600s](https://tex.z-dn.net/?f=time%3D%5Cfrac%7Bmass%2A%28v-v_%7Bo%7D%29%7D%7BForce%7D%5C%5C%5C%5Ctime%3D%5Cfrac%7B72000%2A%2863%5Cfrac%7Bm%7D%7Bs%7D%20-0%29%7D%7B35%5Cfrac%7BKg.m%7D%7Bs%5E%7B2%7D%7D%7D%3D129600s)
Hence, we have:
Variables: Time
Equations:
![Force=mass*aacceleration=mass*\frac{v-v_{o}}{time} \\\\time=\frac{mass*(v-v_{o})}{Force}](https://tex.z-dn.net/?f=Force%3Dmass%2Aaacceleration%3Dmass%2A%5Cfrac%7Bv-v_%7Bo%7D%7D%7Btime%7D%20%5C%5C%5C%5Ctime%3D%5Cfrac%7Bmass%2A%28v-v_%7Bo%7D%29%7D%7BForce%7D)
Answers: The rocket should be fired for 129600 seconds.
Have a nice day!