Question

The stoplight had just changed and a 2100 kg Cadillac had entered the intersection, heading north at 3.2 m/s , when it was struck by a 1100 kg eastbound Volkswagen. The cars stuck together and slid to a halt, leaving skid marks angled 35° north of east. How fast was the Volkswagen going just before the impact?

Answer 1

Explanation:

It is given that,

Mass of the Cadillac, $m_1=2100\ kg$

Speed of Cadillac, $v_1=3.2\ m/s$ (towards north)

Mass of Volkswagen, $m_2=1100\ kg$

The cars stuck together and slid to a halt, leaving skid marks angled 35 degrees north of east.

According to the law of conservation of momentum,

The momentum along x axis, $m_1v_1=(m_1+m_2)\ usin35$............(1)

The momentum along y axis, $m_2v_2=(m_1+m_2)\ ucos35$...........(2)

From equation (1) and (2) it is clear that,

$\dfrac{m_1v_1}{m_2v_2}=tan35$

$v_2=\dfrac{m_1v_1}{m_2\ tan35}$

$v_2=\dfrac{2100\times 3.2}{1100\times \ tan35}$

$v_2=8.72\ m/s$

So, the Volkswagen going just before the impact is 8.72 m/s. Hence, this is the required solution.