|Momentum| = (mass) x (speed)
225 kg-m/s =(50kg) x (speed)
Divide each side by (50kg): Speed=(225 kg-m/s) / (50 kg) = 4.5 m/s .
Regarding the velocity, nothing can be said other than the speed, because
we have no information regarding the direction of the object's motion.
<u>Answer:</u> The velocity of released alpha particle is ![1.127\times 10^7m/s](https://tex.z-dn.net/?f=1.127%5Ctimes%2010%5E7m%2Fs)
<u>Explanation:</u>
According to law of conservation of momentum, momentum can neither be created nor be destroyed until and unless, an external force is applied.
For a system:
![m_1v_1=m_2v_2](https://tex.z-dn.net/?f=m_1v_1%3Dm_2v_2)
where,
= Initial mass and velocity
= Final mass and velocity
We are given:
![m_1=238u\\v_1=1.895\times 10^{5}m/s\\m_2=4u\text{ (Mass of }\alpha \text{ -particle)}\\v_2=?m/s](https://tex.z-dn.net/?f=m_1%3D238u%5C%5Cv_1%3D1.895%5Ctimes%2010%5E%7B5%7Dm%2Fs%5C%5Cm_2%3D4u%5Ctext%7B%20%28Mass%20of%20%7D%5Calpha%20%5Ctext%7B%20-particle%29%7D%5C%5Cv_2%3D%3Fm%2Fs)
Putting values in above equation, we get:
![238\times 1.895\times 10^5=4\times v_2\\\\v_2=\frac{238\times 1.895\times 10^5}{4}=1.127\times 10^7m/s](https://tex.z-dn.net/?f=238%5Ctimes%201.895%5Ctimes%2010%5E5%3D4%5Ctimes%20v_2%5C%5C%5C%5Cv_2%3D%5Cfrac%7B238%5Ctimes%201.895%5Ctimes%2010%5E5%7D%7B4%7D%3D1.127%5Ctimes%2010%5E7m%2Fs)
Hence, the velocity of released alpha particle is ![1.127\times 10^7m/s](https://tex.z-dn.net/?f=1.127%5Ctimes%2010%5E7m%2Fs)
Answer:
The height reached is 20m, The time taken to reach 20m is 2 seconds
Explanation:
Observing the equations of motion we can see that the following equation will be most helpful for this question.
![v^{2} = u^{2} + 2as](https://tex.z-dn.net/?f=v%5E%7B2%7D%20%3D%20u%5E%7B2%7D%20%2B%202as)
We are given initial velocity, u
We know that the stone will stop at its maximum height, so final velocity, v
Acceleration, a
And we are looking for the displacement (height reached), s
Substitute the values we are given into the equation
![0^{2} = 20^{2} + 2(10)s](https://tex.z-dn.net/?f=0%5E%7B2%7D%20%3D%2020%5E%7B2%7D%20%2B%202%2810%29s)
Rearrange for s
![0^{2} -20^{2} =20s](https://tex.z-dn.net/?f=0%5E%7B2%7D%20-20%5E%7B2%7D%20%3D20s)
![-400=20s](https://tex.z-dn.net/?f=-400%3D20s)
![\frac{-400}{20} =s](https://tex.z-dn.net/?f=%5Cfrac%7B-400%7D%7B20%7D%20%3Ds)
s = -20 (The negative is just showing direction, it can be ignored for now)
The height reached is 20m
Use a different equation to find the time taken
![s = vt - \frac{1}{2} at^{2}](https://tex.z-dn.net/?f=s%20%3D%20vt%20-%20%5Cfrac%7B1%7D%7B2%7D%20at%5E%7B2%7D)
Substitute in the values we have
![-20=(0)t - \frac{1}{2} (10)t^{2}](https://tex.z-dn.net/?f=-20%3D%280%29t%20-%20%5Cfrac%7B1%7D%7B2%7D%20%2810%29t%5E%7B2%7D)
Rearrange for t
![-20 =0 -5 t^{2}](https://tex.z-dn.net/?f=-20%20%3D0%20-5%20t%5E%7B2%7D)
![\frac{-20}{-5} =t^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-20%7D%7B-5%7D%20%3Dt%5E%7B2%7D)
![4 = t^{2}](https://tex.z-dn.net/?f=4%20%3D%20t%5E%7B2%7D)
t = 2s
The time taken to reach 20m is 2 seconds
Answer:
William Ferrel created a tide-prediction machine.
Explanation:
- William Ferrel create a machine in late 19th century that was the best combination of mechanical parts and computer coding.
- It was a mechanical analog computer that could predict the ebb of tides and even the height of tides that could be irregular.
- It was widely used for marine networks and navigation. Later on many improvisations and additional features were added on it.
- During the world war times, this tide prediction machine was of great use for military purpose.