
(a)
To Sketch: The situation, assigning coordinate axes and identifying “before” and “after”.
(a)

Explanation of Solution
Introduction:
The situation can be sketched by applying the conservation of momentum and the notation of vectors.
According the conservation of momentum,
Total initial momentum = total final momentum
To sketch the problem showing the states before and after collision, take the y-axis as north and the x-axis as East.
Before the collision, a compact car is shown by a vector which is heading towards the south while the full - sized car is represented by a vector which is heading towards the east.
After the collision, both cars would move as a wreck with a common velocity in southeast direction which is represented by a single vector.
Conclusion:
Hence, the sketch has been drawn.
(b)
To Find: The direction and speed of the wreck.
(b)

Answer to Problem 114A
Explanation of Solution
Given:
Mas of compact car,
Mass of full-sized car,
Initial speed of compact car,
Initial speed of full − sized car,
Formula Used:
Velocity of an object is
Here,
Momentum of the car is given by
Here,
Calculation:
The x-component of the initial momentum of the system will be the sum of the x-components of the momentum of each car. Since the car moving south has no x-component,
Substitute
The y-component of the initial momentum is
Substitute
By the law of conservation of momentum, it can be written as,
And,
Using the vector diagram, it can be written as,
Substitute
The direction of momentum is given by
Substitute
Now, to find the velocity
Substitute
Thus, the wreck at an angle of
Conclusion:
Hence, the wreck is at an angle of
(c)
To Find: The distance travelled by the wreck.
(c)

Answer to Problem 114A
Explanation of Solution
Given:
Coefficient of kinetics friction,
Initial velocity of wreck,
Final velocity of wreck,
Formula Used:
Newton’s second law:
Where,
Friction force:
Where,
Calculation:
Let
The wreck will come to a stop when the fractional force equivalent to the net force acting on it.
Therefore,
Plugging in the given values:
Since, the wreck comes to a stop, Therefore, acceleration would be negative
The distance covered can be determined by using the formula
Plugging in the given values:
Conclusion:
Hence, the wreck skids
Chapter 13 Solutions
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