Final answer:
The magnitude of the resultant momentum of the car after a collision can be calculated using the Pythagorean theorem and is found to be 10.8 meters/second, therefore the correct answer is C. 10.8 meters/second.
Step-by-step explanation:
To find the magnitude of the resultant momentum of a car after a collision when given the x-component and y-component of its momentum, you can use the Pythagorean theorem because momentum is a vector quantity. The x-component of the momentum is 9.80 meters/second, and the y-component is 4.50 meters/second.
Using the Pythagorean theorem, the magnitude of the resultant momentum (p) is given by:
\( p = \sqrt{p_x^2 + p_y^2} \)
\( p = \sqrt{9.80^2 + 4.50^2} \)
\( p = \sqrt{96.04 + 20.25} \)
\( p = \sqrt{116.29} \)
\( p = 10.8 \) meters/second
Therefore, the correct answer is C. 10.8 meters/second.