[tex]\begin{gathered} \text{For the }friction\text{ of mini van} \\ \text{Total mass} \\ m_V=1,700.0\text{ kg+}72.0\text{ kg+ }2(35.0\operatorname{kg})+19(2.80\operatorname{kg}) \\ m_V=1,895.2\text{ kg} \\ From\text{ the fre}e\text{ body diagram of mini van} \\ \uparrow+\Sigma Fy=0 \\ N-m_Vg=0 \\ N=m_Vg \\ g=9.81m/s^2 \\ N=(1,895.2\text{ kg})(9.81m/s^2) \\ N=18,591.9\text{ N} \\ \rightarrow+\Sigma Fx=m_Va \\ -Ff=m_Va \\ a=\frac{-Ff}{m_V} \\ Ff=N\mu_s \\ \mu_s=0.85 \\ Ff=(18,591.9\text{ N})(0.85) \\ Ff=15,803.1\text{ N} \\ \text{The friction force of the mini van is }15,803.1\text{ N} \\ \text{Now, the acceleration of the mini van} \\ a=\frac{-15,803.1\text{ N}}{1,895.2\text{ kg}_{}} \\ a=-8.34m/s^2 \\ \text{The acceleration of the mini van is }-8.34m/s^2 \\ \\ To\text{ find the initial velocity of the van, not final} \\ x=\text{ lenght of the skid mark} \\ x=22m \\ v^2_{fV}=v^2_{oV}+2ax \\ v_{fV}=\text{ 0 m/s because }it\text{ has already stopped moving} \\ (\text{ 0 m/s })^2=v^2_{oV}+2(-8.34m/s^2)(22m),\text{ } \\ 0\text{ }m^2/s^2=v^2_{oV}-366.96\text{ }m^2/s^2 \\ v^2_{oV}=0\text{ }m^2/s^2+366.96\text{ }m^2/s^2 \\ v^2_{oV}=366.96\text{ }m^2/s^2 \\ v_{oV}=\sqrt{366.96\text{ }m^2/s^2} \\ v_{oV}=19.2\text{ m/s} \\ \text{The initial velocity of the van (just after the collision) is }19.2\text{ m/s} \\ \\ To\text{ find the momentum of mini van} \\ P_V=m_Vv_{oV} \\ P_V=(1,895.2\text{ kg})(19.2\text{ m/s}) \\ P_V=36,387.8\text{ kgm/s} \\ \text{This is momentum that }Hummer\text{ has} \\ P_H=36,387.8\text{ kgm/s} \\ \text{But} \\ P_H=m_Hv_H \\ \text{Solving the velocity of th Hummer} \\ v_H=\frac{P_H}{m_H} \\ m_H=1,150.0\text{ }kg+62.0\text{ kg+}7(2.80\operatorname{kg}) \\ m_H=1,231.6\text{ }kg \\ \text{Hence} \\ v_H=\frac{36,387.8\text{ kgm/s}}{1,231.6\text{ }kg_{}} \\ v_H=29.55\text{ m/s} \\ \text{The velocity of the Hummer is }29.55\text{ m/s} \end{gathered}[/tex]
