Question

A kicker on the football field kicked the ball with an initial velocity of 25.0 m/s at an angle of 30.0 degrees to the horizontal. Which of the following pairs of horizontal and vertical components would represent the velocity vector described above?

a) vx = 25 m/s; vy = 0 m/s
b) vx = 21.7 m/s; vy = 12.5 m/s
c) vx = 12.5 m/s; vy = 21.7 m/s
d) vx = 0 m/s; vy = 25 m/s

Answer 1

The correct pair of horizontal and vertical components for a football kicked with a velocity of 25.0 m/s at an angle of 30.0 degrees is 21.7 m/s for the horizontal component and 12.5 m/s for the vertical component, corresponding to option b).

Step-by-step explanation:

To determine which pair of horizontal and vertical components represent the velocity vector of a football being kicked at an initial velocity of 25.0 m/s at an angle of 30.0 degrees to the horizontal, we need to use trigonometric functions. The horizontal component (vx) can be found using cosine, and the vertical component (vy) can be found using sine.

Therefore:

• vx = v * cos(θ) = 25.0 m/s * cos(30.0°) = 21.7 m/s
• vy = v * sin(θ) = 25.0 m/s * sin(30.0°) = 12.5 m/s

With these calculations, we see that the correct components are 21.7 m/s for horizontal velocity and 12.5 m/s for vertical velocity, which corresponds to option b).