Answer:
![\Delta KE=8.67958\ J](https://tex.z-dn.net/?f=%5CDelta%20KE%3D8.67958%5C%20J)
Explanation:
Given:
- mass of the first ball,
![m_1=2\ kg](https://tex.z-dn.net/?f=m_1%3D2%5C%20kg)
- initial velocity of the first ball,
![u_1=9\ m.s^{-1}](https://tex.z-dn.net/?f=u_1%3D9%5C%20m.s%5E%7B-1%7D)
- mass of the second ball,
![m_2=6.2\ kg](https://tex.z-dn.net/?f=m_2%3D6.2%5C%20kg)
- initial velocity of the second ball,
![u_2= 4\ m.s^{-1}](https://tex.z-dn.net/?f=u_2%3D%204%5C%20m.s%5E%7B-1%7D)
- Final velocity of the first ball,
![v_1=8\ m.s^{-1}](https://tex.z-dn.net/?f=v_1%3D8%5C%20m.s%5E%7B-1%7D)
<u>Using the law of conservation of linear momentum:</u>
![m_1.u_1+m_2.u_2=m_1.v_1+m_2.v_2](https://tex.z-dn.net/?f=m_1.u_1%2Bm_2.u_2%3Dm_1.v_1%2Bm_2.v_2)
where:
final velocity of the second ball
![2\times 9+6.2\times 4=2\times 8+6.2\times v_2](https://tex.z-dn.net/?f=2%5Ctimes%209%2B6.2%5Ctimes%204%3D2%5Ctimes%208%2B6.2%5Ctimes%20v_2)
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<u>Now the kinetic energy lost in the collision:</u>
Δ KE = (Sum of initial individual kinetic energy) - (Sum of individual final kinetic energy)
![\Delta KE=\frac{1}{2} m_1.u_1^2+\frac{1}{2} m_2.u_2^2-(\frac{1}{2} m_1.v_1^2+\frac{1}{2} m_1.v_2^2)](https://tex.z-dn.net/?f=%5CDelta%20KE%3D%5Cfrac%7B1%7D%7B2%7D%20m_1.u_1%5E2%2B%5Cfrac%7B1%7D%7B2%7D%20m_2.u_2%5E2-%28%5Cfrac%7B1%7D%7B2%7D%20m_1.v_1%5E2%2B%5Cfrac%7B1%7D%7B2%7D%20m_1.v_2%5E2%29)
![\Delta KE=0.5\times 2\times 9^2+0.5\times 6.2\times 4^2-(0.5\times 2\times 8^2+0.5\times 6.2\times 4.3225^2)](https://tex.z-dn.net/?f=%5CDelta%20KE%3D0.5%5Ctimes%202%5Ctimes%209%5E2%2B0.5%5Ctimes%206.2%5Ctimes%204%5E2-%280.5%5Ctimes%202%5Ctimes%208%5E2%2B0.5%5Ctimes%206.2%5Ctimes%204.3225%5E2%29)
![\Delta KE=8.67958\ J](https://tex.z-dn.net/?f=%5CDelta%20KE%3D8.67958%5C%20J)
<h2>
Option 3, 216 m is the correct answer.</h2>
Explanation:
We have initial velocity, u = 15 m/s
Time, t = 12 seconds
Final velocity, v = 21 m/s
We have equation of motion v = u + at
Substituting
21 = 15 + a x 12
a = 0.5 m/s²
Now we have equation of motion v² = u² + 2as
21² = 15² + 2 x 0.5 x s
s = 216 m
Displacement = 216 m
Option 3, 216 m is the correct answer.
False, There are no genetics that can save you from constant overeating and there are no genetics that can prevent you from working out, at least to your possible extent.
The velocity at the maximum height will always be 0. Therefore, you will count your final velocity as 0, and your initial velocity as 35 m/s. Next, we know that the acceleration will be 9.8 m/s^2. How? Because the ball is thrown directly upward, and the only force acting on it will be the force of gravity pushing it back down.
The formula we use is h = (Vf^2 - Vi^2) / (2*-9.8m/s^2)
Plugging everything in, we have h = (0-1225)/(19.6) = 62.5 meters is the maximum height.