The horizontal component of the initial velocity can be found using the following formula:

$v_{x} = v_0 \cdot \cos(\theta)$

Where:

• $v_0 = 32 \, \text{m/s}$ is the initial velocity,
• $\theta = 66.7^\circ$ is the launch angle.

Now, calculating $v_x$:

$v_{x} = 32 \cdot \cos(66.7^\circ)$

Let me calculate that for you.The horizontal component of the initial velocity is approximately $12.66 \, \text{m/s}$.

Would you like more details or have any questions about this calculation?

Here are 5 related questions to explore further:

1. What is the vertical component of the initial velocity?
2. How long will the projectile be in the air?
3. What is the maximum height reached by the projectile?
4. How far horizontally will the projectile travel before hitting the ground?
5. What are the effects of air resistance on the projectile’s trajectory?

Tip: When breaking velocity into components, always use the correct trigonometric functions—cosine for horizontal and sine for vertical components.