Answer:
a. [tex]v_f=1.477m/s[/tex]
b. Δ[tex]K=1558.3J[/tex]
c. [tex]E_k=1034.7 J[/tex]
Explanation:
a).
Momentum conserved
[tex]p_{ix}=p_{fx}[/tex]
[tex]m_1*v_1+m_2*v_2=(m_1+m_2)*v_f[/tex]
[tex]v_f=\frac{m_1*v_1+m_2*v_2}{m_1+m_2}[/tex]
[tex]v_f=\frac{89.0kg*5.6m/s+85.0kg*-2.84m/s}{(89.0+85.0)kg}[/tex]
[tex]v_f=1.477m/s[/tex]
b).
Δ[tex]K=K_i-K_f[/tex]
[tex]\frac{1}{2}*m_1*v_1^2+\frac{1}{2}*m_2*v_2^2=\frac{1}{2}*(m_1+m_2)*v_f^2[/tex]
[tex]\frac{1}{2}*89.0kg*(5.6m/s)^2+\frac{1}{2}*85.0kg*(2.84m/s)^2=\frac{1}{2}*(89.0+85.0)kg*(1.447m/s)^2[/tex]
Δ[tex]K=1558.3J[/tex]
c).
[tex]E_k=\frac{1}{2}*89kg*(5.8m/s)^2-\frac{1}{2}*(85+89)kg*(1.44m/s)^2[/tex]
[tex]E_k=1034.7 J[/tex]
d).
All of which has been lost as mechanical energy, and is now thermal energy warmer football players, noise a loud crunch for example.
