To determine the horizontal component of the initial velocity of a ball kicked at an angle, follow these steps:
1. Understand the given values:
- Initial velocity ([tex]\(v_0\)[/tex]): 16 m/s
- Angle of launch ([tex]\(\theta\)[/tex]): 40° relative to the ground
2. Convert the angle from degrees to radians:
- To do this, use the conversion factor where [tex]\(180^\circ = \pi \ \text{radians}\)[/tex].
- The formula to convert degrees to radians is:
[tex]\[
\theta_\text{radians} = \theta_\text{degrees} \times \frac{\pi}{180}
\][/tex]
- Plugging in the values, we get:
[tex]\[
\theta_\text{radians} \approx 40 \times \frac{\pi}{180} \approx 0.6981 \ \text{radians}
\][/tex]
3. Calculate the horizontal component of the initial velocity:
- The horizontal component of the initial velocity ([tex]\(v_{0x}\)[/tex]) can be found using the cosine function. The formula is:
[tex]\[
v_{0x} = v_0 \cos(\theta_\text{radians})
\][/tex]
- Given the initial velocity of 16 m/s and the angle in radians (approximately 0.6981), we can calculate:
[tex]\[
v_{0x} \approx 16 \cos(0.6981) \approx 12.3 \ \text{m/s}
\][/tex]
Therefore, the approximate horizontal component of the initial velocity is 12.3 m/s. From the given options, the correct answer is:
O 12.3 m/s
