Answer:
10.89 seconds
229.895 m
Explanation:
Distance van travels
[tex]x_v=170+5.5t+\dfrac{1}{2}0t^2\\\Rightarrow x_v=170+5.5t[/tex]
Position of car
[tex]x_c=0+32t+\dfrac{1}{2}-2t^2\\\Rightarrow x_c=32t-t^2[/tex]
They are equal
[tex]170+5.5t=32t-t^2\\\Rightarrow 17+5.5t-32t+t^2\\\Rightarrow t^2-26.5t+170=0\\\Rightarrow 10t^2-265t+1700=0[/tex]
[tex]t=\frac{-\left(-265\right)+\sqrt{\left(-265\right)^2-4\cdot \:10\cdot \:1700}}{2\cdot \:10}, \frac{-\left(-265\right)-\sqrt{\left(-265\right)^2-4\cdot \:10\cdot \:1700}}{2\cdot \:10}\\\Rightarrow t=15.6, 10.89\ s[/tex]
The collision occurs at 10.89 seconds
[tex]x_v=170+5.5\times 10.89\\\Rightarrow x_v=229.895\ m[/tex]
Collision occurs at 229.895 m from the starting point
