Question

The stoplight had just changed and a 2000 kg Cadillac had entered the intersection, heading north at 3.0 m/s, when it was struck by a 1000 kg eastbound Volkswagen. The cars stuck together and slid to a halt, leaving skid marks angled 35° north of east. How fast was Volkswagen going just before the impact?

Short answer

The speed of Volkswagen just before the impact is$8.57m/s$

Step-by-step solution

Given information

We need to the speed of Volkswagen going just before the impact.

Analyze and calculate

Consider that Volkswagen is heading positive direction of $x-axis$and Cadilac is heading in a positive direction of $y-axis$. When they crash, their velocity is

$\overrightarrow{V_{final}}=\cos \left(35°\right)V_{final}\overrightarrow{i}+\sin \left(35°\right)V_{final}\overrightarrow{j}$

From the law of conservation of momentum for $x$and $y-axis$:

$$\begin{gathered} y-axis: \\ {m}_{Cadilac}{v}_{Cardilac}=\sin \left(35°\right)(m_{Cardilac}+m_{Volkswagen})v_{final} \\ {v}_{final}=3.49m/s \end{gathered}$$

$$\begin{gathered} x-axis: \\ {m}_{Valkswagen}{v}_{Valkswagen}=\cos \left(35°\right)(m_{Cardilac}+m_{Valkswagen})v_{final} \\ {v}_{Valkswagen}=8.57m/s \end{gathered}$$