A river flows toward the east at 1.7 m/s. Steve can swim 2.0 m/s in still water. If he swims relative to the water at a direction of 33 degrees west of north, how long will it take him to cross the 75 m wide river?
A) 45 s
B) 39 s
C) 123 s
D) 27 s

Question

Quizplus · Accepted Answer

The correct answer is A.Explanation:The velocity of the river is 1.7 m/s towards the east. Steve's velocity relative to the water is 2.0 m/s at a direction of 33 degrees west of north. We can use the following equation to find the time it takes Steve to cross the river:```time = distance / velocity```The distance across the river is 75 m. The velocity of Steve relative to the ground is the vector sum of his velocity relative to the water and the velocity of the river. We can use the following equation to find the magnitude of the velocity of Steve relative to the ground:```velocity = sqrt((velocity_water_x + velocity_river_x)^2 + (velocity_water_y + velocity_river_y)^2)```where:* velocity_water_x is the x-component of Steve's velocity relative to the water* velocity_water_y is the y-component of Steve's velocity relative to the water* velocity_river_x is the x-component of the river's velocity* velocity_river_y is the y-component of the river's velocityThe x-component of Steve's velocity relative to the water is:```velocity_water_x = 2.0 * cos(33 degrees) = 1.66 m/s```The y-component of Steve's velocity relative to the water is:```velocity_water_y = 2.0 * sin(33 degrees) = 1.15 m/s```The x-component of the river's velocity is:```velocity_river_x = 1.7 m/s```The y-component of the river's velocity is:```velocity_river_y = 0 m/s```The magnitude of the velocity of Steve relative to the ground is:```velocity = sqrt((1.66 m/s + 1.7 m/s)^2 + (1.15 m/s + 0 m/s)^2) = 3.32 m/s```The time it takes Steve to cross the river is:```time = 75 m / 3.32 m/s = 22.6 s```Therefore, the correct answer is A.

A River Flows Toward the East at 1