This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given velocities. The velocity of the current, v_c, is 0.54 m/s from right to left. The velocity of the swimmer relative to the water, v_sw, is 0.72 m/s at right angles to the current. Step 2: Calculate the magnitude of the swimmer's velocity relative to the river bank. Since the two velocities are perpendicular, we can use the Pythagorean theorem to find the magnitude of the resultant velocity, v_s. |v_s| = sqrt(|v)_sw|^2 + |v_c|^2 |v_s| = sqrt((0.72 m/s))^2 + (0.54 m/s)^2 |v_s| = sqrt(0.5184 m)^2/s^2 + 0.2916 m^2/s^2 |v_s| = sqrt(0.81 m)^2/s^2 |v_s| = 0.90 m/s Step 3: Calculate the direction of the swimmer's velocity relative to the river bank. Let be the angle of the swimmer's resultant velocity relative to the direction the swimmer is aiming (perpendicular to the current). = velocity component parallel to currentvelocity component perpendicular to current = |v_c||v_sw| = 0.54 m/s0.72 m/s = (3)/(4) = 0.75 = (0.75) ≈ 36.9^ The swimmer is swimming perpendicular to the current, and the current is flowing from right to left. Therefore, the resultant velocity will be directed 36.9^ from the direction perpendicular to the current, towards the left bank (in the direction of the current). The magnitude of the swimmer's velocity relative to the river bank is 0.90 m/s. The direction of the swimmer's velocity relative to the river bank is 36.9^ from the direction perpendicular to the current, towards the left bank.