To find the possible values of [tex]\( v_x \)[/tex] for an object traveling with a velocity [tex]\( v = 4.0 \)[/tex] meters/second at an angle of [tex]\( 60^\circ \)[/tex] with the positive direction of the [tex]\( y \)[/tex]-axis, we need to follow these steps:
1. Convert the Angle: The given angle is [tex]\( 60^\circ \)[/tex]. The trigonometric calculations are usually done using radians, but the key point here is understanding the provided angle relative to the axes.
2. Identify the Components:
- The angle is with respect to the positive [tex]\( y \)[/tex]-axis. Usually, we use angles with respect to the [tex]\( x \)[/tex]-axis, but we can adapt for this case.
- If [tex]\( 60^\circ \)[/tex] is the angle with the positive [tex]\( y \)[/tex]-axis, it implies we are essentially dealing with a 30° angle with respect to the negative [tex]\( x \)[/tex]-axis since any angle can be broken into its complementary components.
3. Break Down the Velocity Component: The x-component (horizontal) of the velocity [tex]\( v_x \)[/tex] can be found using the cosine function.
- [tex]\( v_x = v \cdot \sin(60^\circ) \)[/tex]
- Given that [tex]\( \sin(60^\circ) \)[/tex] is approximately [tex]\( \sqrt{3}/2 \approx 0.866 \)[/tex]
4. Calculate [tex]\( v_x \)[/tex]:
- [tex]\( v_x = 4.0 \cdot \frac{\sqrt{3}}{2} \approx 4.0 \cdot 0.866 \approx 3.5 \)[/tex] meters/second.
5. Consider Direction:
- Since velocity can have direction and we specifically need the possible values, there's
- [tex]\( v_x = 3.5 \)[/tex] meters/second in the positive direction, and
- [tex]\( v_x = -3.5 \)[/tex] meters/second in the negative direction.
Thus, the possible values of [tex]\( v_x \)[/tex] are [tex]\( -3.5 \)[/tex] meters/second and [tex]\( +3.5 \)[/tex] meters/second.
So, the correct answer is:
A. -3.5 meters/second and +3.5 meters/second
