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Required information

Problem $14\mathrm{.}019-$ Collision of three cars

Cruiser $\backslash ($ A $\backslash )$ was traveling east at $\backslash ($ X$=69\backslash$mathrm$\{$mi$\}/\backslash$mathrm$\{$h$\}\backslash )$ on a police emergency call when it was hit at an intersection by car $\backslash ($ B $\backslash ),$ which was traveling south at high speed. After sliding together on the wet pavement, the two cars hit cruiser $\backslash ($ C $\backslash ),$ which was traveling north at $\backslash (45\backslash$mathrm$\{$mi$\}/\backslash$mathrm$\{$h$\}\backslash )$ and was $63$ ft from the intersection at the time of the first collision. Stuck together, the three cars hit a wall and came to a stop at $\backslash ($ D $\backslash ).$ Knowing that car $\backslash ($ B $\backslash )$ weighs $3600$ lb and that each of the cruisers weighs $3000$ lb $,$ solve the problems by neglecting the forces exerted on the cars by the wet pavement and treating the cars as point masses.

Problem $14\mathrm{.}019.$b $-$ Speed of one car

Knowing that the coordinates of point $\backslash ($ D $\backslash )$ are $\backslash (\backslash$mathrm$\{$x$\}\_\{\backslash$mathrm$\{$D$\}\}=42\backslash$mathrm$\{$ft$\}\backslash )$ and $\backslash (\backslash$mathrm$\{$y$\}\_\{\backslash$mathrm$\{$D$\}\}=46\mathrm{.}5\backslash$mathrm$\{$ft$\}\backslash ),$ determine the speed of car $\backslash ($ B $\backslash ).$

The speed of car $\backslash ($ B $\backslash )$ is $\backslash (\backslash$mathrm$\{$mi$\}/\backslash$mathrm$\{$h$\}\backslash ).$