a. A river has a steady speed of 0.30 m/s.A student swims downstream a distance

Question

a. A river has a steady speed of 0.30 m/s.A student swims downstream a distance of 1.2 km and returns to thestarting point. If the student swims with respect to the water at aconstant speed and the downstream portion of the swim requires 20minutes, how much time is required for the entire swim? b. A 0.14-km wide river flows with a uniform speed of 4.0 m/stoward the east. It takes 20 s for a boat to cross the river to apoint directly north of its departure point on the south bank. Whatis the speed of the boat relative to the water? a. A river has a steady speed of 0.30 m/s.A student swims downstream a distance of 1.2 km and returns to thestarting point. If the student swims with respect to the water at aconstant speed and the downstream portion of the swim requires 20minutes, how much time is required for the entire swim? b. A 0.14-km wide river flows with a uniform speed of 4.0 m/stoward the east. It takes 20 s for a boat to cross the river to apoint directly north of its departure point on the south bank. Whatis the speed of the boat relative to the water? b. A 0.14-km wide river flows with a uniform speed of 4.0 m/stoward the east. It takes 20 s for a boat to cross the river to apoint directly north of its departure point on the south bank. Whatis the speed of the boat relative to the water?

Explanation / Answer

a. The student swims at the speed of v relative to the water. 20 min =1200 s (v+0.3)m/s * 1200 s = 1200 m ----> v = 0.7 m/s On the way back he swims 1200 m with the speed of v-0.3 during thetime t. (v-0.3)*t = 1200 -----> t = 3000 s This makes the time 3000+1200 = 4200 s = 70 min for the entireswim. b. 140m wide river from south to north. If the boat travels across itin 20 seconds, the average speed of the boat must be 140m / 20s = 7m/s During the trip from the boat also have to move to the west tocancel out the effect of the east-moving river. So the both runs 7 m/s north and 4 m/s west, giving a total speedof (72+42) = 65 m/s (a littlemore than 8 m/s) relative to the water

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