Question

A kicked soccer ball travels 20 m [E], careens off another player, and travels 10 m [60° S of E]. The sum of the x components is:

a) 20 m
b) 10 m
c) 30 m
d) 30√3 m

Answer 1

The sum of the x components is 30 m. Therefore, the correct option is c).

Step-by-step explanation:

To find the sum of the x components, we need to break down the vectors into their horizontal (x) and vertical (y) components. The first vector, 20 m [E], is entirely in the x-direction, so its x component is 20 m. The second vector, 10 m [60° S of E], can be split into its x and y components using trigonometric functions. The x component (horizontal) is given by 10 x cos(60°), which equals
`\(10 * (1)/(2) = 5\)` m. Therefore, the sum of the x components is 20 m + 5 m = 30 m.

The calculation involves using the cosine function to determine the horizontal component of the second vector. The angle of 60 degrees is with respect to the horizontal axis, and the cosine function helps find the adjacent side, which represents the x component. Adding the x components of both vectors gives us the total displacement in the horizontal direction.

In summary, the correct answer is c) 30 m, as it represents the sum of the x components of the two vectors. This calculation is fundamental in vector addition, breaking down motion in different directions to accurately determine the overall displacement.