Final answer:
The average speed of the swimmer with respect to the ground is calculated using the Pythagorean theorem given the swimmer's speed relative to the water and the water's speed, resulting in a speed of approximately 0.943 m/s.
Step-by-step explanation:
The student's question is asking to calculate the average speed of an athlete who swims across a river. To find the speed of the water current in the river, we can use the Pythagorean theorem, since the swimmer's motion relative to the water and the water's motion relative to the ground combine to give the swimmer's motion over the ground. This forms a right-angled triangle. The swimmer's speed across the river is 0.5 m/s (given as perpendicular to the current), and the distance downstream is 40 m while the river width is 25 m. Using the theorem, we can calculate the speed of the water:
v_water = sqrt((40 m)^2 + (25 m)^2) / (25 m / 0.5 m/s) = 0.8 m/s
The swimmer's speed with respect to the ground is then the hypotenuse of the triangle formed by the swimmer's speed relative to the water and the water's speed relative to the ground, which is already found to be 0.8 m/s.
Therefore, the swimmer's speed with respect to a friend on the ground (the hypotenuse) would be:
v_swimmer_ground = sqrt((0.5 m/s)^2 + (0.8 m/s)^2) = 0.943 m/s