As we have all learned from Newton #3, every action has an equal, opposite reaction.
The force that the football exerts on the kicker's foot is <em>equal</em> to the force with which the kicker's foot impacts the ball. (<em>100 N</em>)
Answer:
3.65 m/s
Explanation:
= Mass of first car = 103 kg
= Mass of second car = 81 kg
= Initial Velocity of first car = 5 m/s
= Initial Velocity of second car = -3.3 m/s
= Velocity of center of mass
For elastic collision
![m_1u_1 + m_2u_2 =(m_1 + m_2)v_c\\\Rightarrow v_c=\frac{m_1u_1 + m_2u_2}{m_1 + m_2}\\\Rightarrow v=\frac{103\times 5 + 81\times -3.3}{103 + 81}\\\Rightarrow v=1.35\ m/s](https://tex.z-dn.net/?f=m_1u_1%20%2B%20m_2u_2%20%3D%28m_1%20%2B%20m_2%29v_c%5C%5C%5CRightarrow%20v_c%3D%5Cfrac%7Bm_1u_1%20%2B%20m_2u_2%7D%7Bm_1%20%2B%20m_2%7D%5C%5C%5CRightarrow%20v%3D%5Cfrac%7B103%5Ctimes%205%20%2B%2081%5Ctimes%20-3.3%7D%7B103%20%2B%2081%7D%5C%5C%5CRightarrow%20v%3D1.35%5C%20m%2Fs)
Velocity of center of mass = 1.35 m/s
![v_1=u_1-v_c\\\Rightarrow v_1=5-1.35=3.65\\\Rightarrow v_1=3.65\ m/s](https://tex.z-dn.net/?f=v_1%3Du_1-v_c%5C%5C%5CRightarrow%20v_1%3D5-1.35%3D3.65%5C%5C%5CRightarrow%20v_1%3D3.65%5C%20m%2Fs)
The final velocity of car 1 is 3.65 m/s
Answer: ![\Large\boxed{0.84~J/g^\circ C}](https://tex.z-dn.net/?f=%5CLarge%5Cboxed%7B0.84~J%2Fg%5E%5Ccirc%20C%7D)
Explanation:
<u>Given information</u>
![Q~(Energy)=99,100~J](https://tex.z-dn.net/?f=Q~%28Energy%29%3D99%2C100~J)
![m=3.47~kg](https://tex.z-dn.net/?f=m%3D3.47~kg)
![\Delta T=(T_{Final}-T_{Initial})=(45-11)=34^\circ C](https://tex.z-dn.net/?f=%5CDelta%20T%3D%28T_%7BFinal%7D-T_%7BInitial%7D%29%3D%2845-11%29%3D34%5E%5Ccirc%20C)
<u>Given formula</u>
![Q=m\times c\times\Delta T](https://tex.z-dn.net/?f=Q%3Dm%5Ctimes%20c%5Ctimes%5CDelta%20T)
![Q=Energy\\m=mass\\c=specific~heat\\\Delta T=Change~in~temperature](https://tex.z-dn.net/?f=Q%3DEnergy%5C%5Cm%3Dmass%5C%5Cc%3Dspecific~heat%5C%5C%5CDelta%20T%3DChange~in~temperature)
<u>Convert the unit of mass into Grams</u>
![1~kg=1000~g\\](https://tex.z-dn.net/?f=1~kg%3D1000~g%5C%5C)
![3.47~kg=3.47\times 1000=3470~g](https://tex.z-dn.net/?f=3.47~kg%3D3.47%5Ctimes%201000%3D3470~g)
<u>Substitute values into the given formula</u>
![(99100)=(3470)\times c \times(34)](https://tex.z-dn.net/?f=%2899100%29%3D%283470%29%5Ctimes%20c%20%5Ctimes%2834%29)
<u>Simplify by multiplication</u>
![99100=117980~c](https://tex.z-dn.net/?f=99100%3D117980~c)
<u>Divide 117980 on both sides</u>
![99100\div117980=117980~c\div117980](https://tex.z-dn.net/?f=99100%5Cdiv117980%3D117980~c%5Cdiv117980)
![\Large\boxed{c=0.84~J/g^\circ C}](https://tex.z-dn.net/?f=%5CLarge%5Cboxed%7Bc%3D0.84~J%2Fg%5E%5Ccirc%20C%7D)
Hope this helps!! :)
Please let me know if you have any questions
The force needed is 5250N