To determine the angle of the motion of the two vehicles with respect to the x-axis after they collided and stuck together, we can follow these steps:
1. Understand the given data:
- [tex]\(y\)[/tex]-momentum ([tex]\(p_y\)[/tex]) = [tex]\(2.40 \times 10^4 \)[/tex] kilogram meters/second
- [tex]\(x\)[/tex]-momentum ([tex]\(p_x\)[/tex]) = [tex]\(7.00 \times 10^4 \)[/tex] kilogram meters/second
2. Calculate the angle [tex]\(\theta\)[/tex] of the resultant momentum vector with respect to the x-axis:
- We use the tangent function, [tex]\(\tan(\theta) = \frac{p_y}{p_x}\)[/tex].
- So, [tex]\(\theta = \tan^{-1}\left(\frac{p_y}{p_x}\right)\)[/tex].
3. Input the given momenta:
- [tex]\(\frac{p_y}{p_x} = \frac{2.40 \times 10^4}{7.00 \times 10^4}\)[/tex].
- Simplify: [tex]\(\frac{p_y}{p_x} = \frac{2.40}{7.00} \approx 0.3428571\)[/tex].
4. Find the angle [tex]\(\theta\)[/tex] in radians:
- [tex]\(\theta = \tan^{-1}(0.3428571)\)[/tex].
5. Convert the angle from radians to degrees to make it more interpretable:
- The result from the calculations gives us approximately: [tex]\(\theta \approx 0.3303\)[/tex] radians.
- Convert to degrees: [tex]\(\theta \approx 0.3303 \times \frac{180}{\pi} \approx 18.9246\)[/tex] degrees.
6. Compare the calculated degree value to the given answers:
- From the options provided, the closest value to [tex]\(18.9246^{\circ}\)[/tex] is clearly [tex]\(18.9^{\circ}\)[/tex].
Therefore, the correct answer is [tex]\( \boxed{18.9^{\circ}} \)[/tex].
