Q. 58 The stoplight had just changed a... [FREE SOLUTION]

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Chapter 11: Q. 58 (page 290)

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掳 north of east. How fast was Volkswagen going just before the impact?

Short Answer

Expert verified

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

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 $x - a x i s$ and Cadilac is heading in a positive direction of $y - a x i s$ . When they crash, their velocity is

$\overset{鈫�}{V_{f i n a l}} = \cos (35 掳) V_{f i n a l} \overset{鈫�}{i} + \sin (35 掳) V_{f i n a l} \overset{鈫�}{j}$

From the law of conservation of momentum for $x$ and $y - a x i s$ :

$y - a x i s : m_{C a d i l a c} v_{C a r d i l a c} = \sin (35 掳) (m_{C a r d i l a c} + m_{V o l k s w a g e n}) v_{f i n a l} v_{f i n a l} = 3.49 m / s$

$x - a x i s : m_{V a l k s w a g e n} v_{V a l k s w a g e n} = \cos (35 掳) (m_{C a r d i l a c} + m_{V a l k s w a g e n}) v_{f i n a l} v_{V a l k s w a g e n} = 8.57 m / s$