Final answer:
The student's question involves calculating the distance a swimmer will be carried downstream while crossing a river due to the current. The distance downstream will equal the river's current speed multiplied by the time taken to cross. If the swimmer's speed is 0.5 m/s, similar to the athlete in the given examples, she will land 65 meters downstream from her starting point.
Step-by-step explanation:
The question involves a calculation related to the effects of a current on an object moving across a river, which is a classic problem in relative motion in physics. In this scenario, a swimmer is crossing a 65-meter wide river with a current of 0.50 meters per second. The swimmer aims her body directly across the river but the current will still carry her downstream. To find out how far downstream she will land from her starting point, we need to use the Pythagorean theorem and knowledge of vectors to determine the resultant motion.
Since the swimmer is heading straight across and the river's current is perpendicular to her motion, we can consider the downstream motion and the swimmer's forward motion as two separate and perpendicular vector components. She would travel the 65 meters across the river at her own speed, unaltered by current (since it's perpendicular), and at the same time, the current would carry her downstream. If the swimmer's speed isn't provided, we can't calculate the time or the exact distance downstream, as it depends on the time taken to cross 65 meters.
However, if we assume she has the same speed as the athlete in the example information provided (0.5 m/s), we could calculate the time and the downstream distance. The time (t) to cross the river would be the width of the river (65 m) divided by the swimmer's speed (0.5 m/s), which yields t = 130 s. During this time, the current would carry her downstream a distance of 0.50 m/s * 130 s = 65 m. So, if she swims at 0.5 m/s, she would land exactly 65 meters downstream from her starting point.