Final answer:
To find the x-component of the skater's acceleration, we calculate the initial and final x-components of velocity and then divide the change in velocity by the time interval. The skater's x-component of acceleration is approximately -0.453 m/s².
Step-by-step explanation:
To calculate the x-component of the ice skater's acceleration, we first determine the initial and final velocities in the x-direction. The initial velocity in the x-direction (vix) is the initial velocity times the cosine of the initial angle, which is 2.25 m/s * cos(50°) = 2.25 m/s * 0.6428 = 1.4463 m/s. Similarly, the final velocity in the x-direction (vfx) is given by 4.65 m/s * cos(120°) = 4.65 m/s * (-0.5) = -2.325 m/s.
To find the x-component of the acceleration (ax), we use the formula a = (vf - vi) / t, where vf is the final velocity, vi is the initial velocity, and t is the time. Substituting the x-components and the time gives us ax = (vfx - vix) / t = (-2.325 m/s - 1.4463 m/s) / 8.33 s = -3.7713 m/s² / 8.33 s = -0.4527 m/s². The x-component of the skater's acceleration is approximately -0.453 m/s².