The mechanical energy for the first and the second ball is
![10 ^{7} \: joules.](https://tex.z-dn.net/?f=10%20%5E%7B7%7D%20%20%5C%3A%20joules.)
Mass of the first ball = 20 kg
The initial speed at which a cannonball is fired from a cannon =1000 m/s
The angle made by the cannonball while being fired from the cannon = 37°
The maximum height reached by the first ball is,
![= \frac{ u {}^{2} _{1}sin {}^{2} θ}{2g}](https://tex.z-dn.net/?f=%20%3D%20%20%20%5Cfrac%7B%20u%20%7B%7D%5E%7B2%7D%20_%7B1%7Dsin%20%7B%7D%5E%7B2%7D%20%CE%B8%7D%7B2g%7D)
![= \frac{ {1000}^{2} sin {}^{2}37°}{2 \times 9.8}](https://tex.z-dn.net/?f=%20%3D%20%20%20%20%5Cfrac%7B%20%7B1000%7D%5E%7B2%7D%20sin%20%7B%7D%5E%7B2%7D37%C2%B0%7D%7B2%20%5Ctimes%209.8%7D)
![= 18478.69 \: m](https://tex.z-dn.net/?f=%20%3D%2018478.69%20%5C%3A%20m)
The maximum height of the first cannonball is 17478.69 m.
The initial speed at which a cannonball is fired from a cannon =1000 m/s
The angle made by the cannonball while being fired from the cannon = 90 °
![= \frac{ u {}^{2} _{2}sin {}^{2} θ}{2g}](https://tex.z-dn.net/?f=%20%3D%20%20%20%5Cfrac%7B%20u%20%7B%7D%5E%7B2%7D%20_%7B2%7Dsin%20%7B%7D%5E%7B2%7D%20%CE%B8%7D%7B2g%7D)
![= \frac{ 1000{}^{2}sin^{2} 90°}{2 \times 9.8}[tex] = 51020.41 \: m](https://tex.z-dn.net/?f=%20%3D%20%20%20%5Cfrac%7B%201000%7B%7D%5E%7B2%7Dsin%5E%7B2%7D%2090%C2%B0%7D%7B2%20%5Ctimes%209.8%7D%5Btex%5D%20%3D%2051020.41%20%5C%3A%20m)
For the first ball, total mechanical energy= Potential energy at maximum height + kinetic energy at the maximum height
So, the total mechanical energy is,
= mgh \: + \frac{1}{2}mv {}^{2} _{x}[/tex]
![= 20 \times 9.8 \times 18478.64 \times \frac{20}{2} (1000 \: cos37 °)](https://tex.z-dn.net/?f=%20%3D%2020%20%5Ctimes%209.8%20%5Ctimes%2018478.64%20%20%5Ctimes%20%20%5Cfrac%7B20%7D%7B2%7D%20%281000%20%5C%3A%20cos37%20%C2%B0%29)
![= 10 ^{7} The potential energy at the maximum height, = m _{2}gh](https://tex.z-dn.net/?f=%3D%2010%20%5E%7B7%7D%20%20%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3EThe%20potential%20energy%20at%20the%20maximum%20height%2C%20%3D%20m%20_%7B2%7Dgh)
![= 20 \times 9.8 \times 51020.41](https://tex.z-dn.net/?f=%20%3D%2020%20%5Ctimes%209.8%20%20%5Ctimes%2051020.41)
![= 10 ^{7} \:J](https://tex.z-dn.net/?f=%20%3D%2010%20%5E%7B7%7D%20%5C%3AJ)
Therefore, the total mechanical energy for the first and the
![\:second \: cannonball \: is \: 10 ^{7} \:joules.](https://tex.z-dn.net/?f=%20%5C%3Asecond%20%5C%3A%20%20%3Cstrong%3Ecannonball%3C%2Fstrong%3E%20%5C%3A%20%20is%20%20%5C%3A%2010%20%5E%7B7%7D%20%20%5C%3Ajoules.)
To know about energy, refer to the below link:
brainly.com/question/1932868
#SPJ4