Final answer:
The exact change in position when the runner is moving directly east cannot be determined with the given information. The process would involve decomposing the initial velocity and acceleration into components, using kinematic equations, and trigonometry to solve for Δx when the runner's motion is eastward.
Step-by-step explanation:
The question is concerned with a runner who moves at 2.88 m/s north and accelerates at 0.350 m/s² at a -52.0 degree angle. We're asked to find the change in position when the runner is moving directly east. To find the change in position (Δx), we would normally use kinematic equations. However, since the acceleration vector is at an angle and we want to know when she is moving directly east, this requires decomposing the initial velocity and acceleration into components and using vector addition.
Unfortunately, without additional information, such as the time during which she accelerates or the total displacement, we can't provide an exact numeric answer. Typically, one would need to know how long the acceleration was applied to calculate the change in position using the formula Δx = v₀t + (1/2)at² where v₀ is the initial velocity, a is the acceleration, and t is the time.
As the exact numeric answer is not available with the information provided, we can instead describe the process: decompose vectors into components, apply kinematic equations, and use trigonometry to find the exact change in position when the runner is moving east.