Question

question 5 1 pts a b 5 m/s 5 m/s 10 m/s 10 m/s figure a and figure b both show two velocity vectors. let \\( \vec{a} \\) and \\( \vec{b} \\) be the vector sums of the velocity vectors in figure a and figure b, respectively. are the speed and the velocity of \\( \vec{a} \\) the same as the speed and velocity of \\( \vec{b} \\)? \\( \bigcirc \\) no, because the vectors are in opposite directions, which means the velocities are different. \\( \bigcirc \\) yes, because both vectors have the same magnitude. \\( \bigcirc \\) yes, because both vectors point in the same direction. \\( \bigcirc \\) no, because \\( \vec{a} \\) has a magnitude of +5m/s and \\( \vec{b} \\) has a magnitude of −5m/s.

Explanation:

1. First, calculate the vector sum for Figure A: Let the right - ward direction be positive. The two vectors are \(- 5\ m/s\) (left - ward) and \(+ 10\ m/s\) (right - ward). The vector sum \(\vec{A}=10 - 5=+ 5\ m/s\) (right - ward).
2. Then, calculate the vector sum for Figure B: The two vectors are \(+ 5\ m/s\) (right - ward) and \(- 10\ m/s\) (left - ward). The vector sum \(\vec{B}=5-10 = - 5\ m/s\) (left - ward).
3. Speed is the magnitude of velocity. The magnitude of \(\vec{A}\) is \(|5| = 5\ m/s\), and the magnitude of \(\vec{B}\) is \(|-5|=5\ m/s\), so the speeds are the same. But velocity is a vector quantity that includes direction. The direction of \(\vec{A}\) is right - ward, and the direction of \(\vec{B}\) is left - ward, so the velocities are different. Among the options, the first option correctly states that the velocities are different because the vectors (velocity vectors) are in opposite directions. The second option is wrong because it only considers magnitude, not direction for velocity. The third option is wrong as the vectors \(\vec{A}\) and \(\vec{B}\) point in opposite directions. The fourth option is wrong in the description of magnitudes (speed is magnitude, and both have a speed of \(5\ m/s\), and the sign in the magnitude description is incorrect as magnitude is non - negative).

Answer:

No, because the vectors are in opposite directions, which means the velocities are different.