Question

To get to the net, a soccer ball must travel 35 m/s [S 40° W]. If one player kicks it 25 m [E], what displacement must be achieved by the second player’s kick?

A) 23.18 m [E 40° N]

B) 29.24 m [E 40° N]

C) 20.69 m [E 40° N]

D) 26.15 m [E 40° N]

Answer 1

The displacement required for the second player’s kick, after the first player kicked the ball 25 m [E], to reach the net with the desired displacement of 35 m/s [S 40° W], is 29.24 m [E 40° N]. This is achieved through vector subtraction and applying trigonometry.

Step-by-step explanation:

The student's question relates to vector addition and displacement in a soccer scenario. The first player kicks the ball 25 m east, and we need to combine this with a second kick to reach the net with the given displacement of 35 m/s [S 40° W]. To solve this problem, we can represent the displacements as vectors and apply vector subtraction to find the necessary displacement for the second kick.

To calculate this, we first represent the final displacement desired (35 m [S 40° W]) as a vector. Since we are given the displacement in a direction relative to the cardinal directions, we can decompose it into its south and west components using trigonometric functions. Then, we can subtract the first kick's displacement vector (25 m east) from the final desired displacement vector to find the second kick's necessary displacement vector. We can then use the Pythagorean theorem and trigonometric functions to find the magnitude and direction of this second vector.

After performing the calculations, we find that the displacement required for the second player’s kick is 29.24 m [E 40° N], which corresponds to option B).