Question

Consider a particle with initial velocity vƒ— that has magnitude 12.0 m/s and is directed 60.0 degrees above the negative x axis. What is the magnitude of the particle's velocity in the x direction?

1) 6.0 m/s
2) 10.4 m/s
3) 12.0 m/s
4) 20.8 m/s

Answer 1

Using trigonometry, specifically the cosine function, the magnitude of the particle's velocity in the x direction is found to be 6.0 m/s.

Step-by-step explanation:

To determine the magnitude of the particle's velocity in the x direction, we need to use trigonometry. Since the particle has an initial velocity directed 60 degrees above the negative x axis, we can use the cosine function to find the x-component of this velocity.

The x-component (vx) of the velocity is given by:

vx = v * cos(θ)

Where:

• v is the magnitude of the initial velocity
• θ is the angle above the negative x-axis, which is 60°

Now, we substitute the given values:

vx = 12.0 m/s * cos(60°)

vx = 12.0 m/s * 0.5

vx = 6.0 m/s

Therefore, the magnitude of the particle's velocity in the x direction is 6.0 m/s.