Final answer:
The possible x components of the velocity vector with a magnitude of 20.0 m/s and y component of -15.0 m/s are 13.23 m/s and -13.23 m/s, as the direction can be either to the left or right in a two-dimensional plane.
Step-by-step explanation:
If a velocity vector has a magnitude of 20.0 m/s and its y component is -15.0 m/s, we can find its x component using the Pythagorean theorem. For a vector with components vx and vy, the magnitude v is given by the equation v = √(vx² + vy²). Given that v = 20.0 m/s and vy = -15.0 m/s, we can rearrange the equation to solve for vx: vx = √(v² - vy²). Substituting the known values:
vx = √(20.0² - (-15.0)²)
vx = √(400 - 225)
vx = √175
vx = 13.23 m/s or vx = -13.23 m/s
The two possible values for the x component are due to the vector's direction in the x-axis, which can be either positive or negative.