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
You're on a roll — Given: Boy's speed in still water, v_b = 1.2 m/s Distance to swim upstream (one way), d = 1 km = 1000 m 1. When the water is still Step 1: Determine the total distance. The boy swims 1 km upstream and returns 1 km downstream. Total distance D = 1000 m + 1000 m = 2000 m. Step 2: Calculate the total time. When the water is still, the boy's speed is simply his speed in still water. T_1 = (D)/(v_b) T_1 = 2000 m1.2 m/s T_1 = (20000)/(12) s T_1 = (5000)/(3) s T_1 ≈ 1666.67 s The total time when the water is still is 1666.67 s. 2. When the water has a steady speed of 0.5 m/s Given water speed, v_w = 0.5 m/s. Step 1: Calculate the speed when swimming upstream. When swimming upstream, the water current opposes the boy's motion. v_up = v_b - v_w v_up = 1.2 m/s - 0.5 m/s v_up = 0.7 m/s Step 2: Calculate the time taken to swim upstream. t_up = (d)/(v_up) t_up = 1000 m0.7 m/s t_up = (10000)/(7) s Step 3: Calculate the speed when swimming downstream. When swimming downstream, the water current aids the boy's motion. v_down = v_b + v_w v_down = 1.2 m/s + 0.5 m/s v_down = 1.7 m/s Step 4: Calculate the time taken to swim downstream. t_down = (d)/(v_down) t_down = 1000 m1.7 m/s t_down = (10000)/(17) s Step 5: Calculate the total time. T_2 = t_up + t_down T_2 = (10000)/(7) s + (10000)/(17) s T_2 = 10000 ((1)/(7) + (1)/(17)) s T_2 = 10000 ((17 + 7)/(7 × 17)) s T_2 = 10000 ((24)/(119)) s T_2 = (240000)/(119) s T_2 ≈ 2016.81 s The total time when the water has a steady speed of 0.5 m/s is 2016.81 s. What's next?