Question 1

1. Solve for the friction force which brought the van to rest after the collision. 2. Solve for the acceleration of the mini van. (This will be negative because the van was moving against the frictional force. 3. Determine the length of skid marks.

1. Solve for the friction force which brought the van to rest after the collision-example-1

1. Solve for the friction force which brought the van to rest after the collision-example-2

1. Solve for the friction force which brought the van to rest after the collision-example-3

Question 2

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

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