Final answer:
The horizontal component of velocity is 6.675 m/s and the vertical component of velocity is 15.6139 m/s.
Step-by-step explanation:
To determine the horizontal and vertical components of the velocity of a football kicked with an initial velocity of 17 m/s at an angle of 67 degrees with the horizontal, we can use trigonometry. The horizontal component of velocity can be found by multiplying the initial velocity by the cosine of the angle. In this case, the horizontal component of velocity is 17 * cos(67) = 17 * 0.3927 = 6.675 m/s. The vertical component of velocity can be found by multiplying the initial velocity by the sine of the angle. In this case, the vertical component of velocity is 17 * sin(67) = 17 * 0.9197 = 15.6139 m/s.