Question

A river running West-to-East has an eastward current of 7 m/s and is 76 meters across North to South); a canoe is crossing the river from South to North at a (Northward) velocity of 3 m/s in an attempt to reach a dock across the river & 112 meters east of his starting location. A.) What is the displacement of the canoe? B.) At what velocity would the person in the canoe have to paddle in order to land at the dock?

Answer 1

The displacement of the canoe can be found by calculating the component of the canoe's velocity perpendicular to the river's current. The time it takes to reach the dock can be calculated by finding the time it takes for the canoe to travel the eastward distance. The person in the canoe would have to paddle at a velocity perpendicular to the river's current to land at the dock.

Step-by-step explanation:

The displacement of the canoe can be calculated by finding the component of the canoe's velocity that is perpendicular to the river's current. Since the river is flowing from west to east, the perpendicular component of the canoe's velocity is its northward velocity of 3 m/s. The displacement can be calculated using the formula: displacement = velocity * time. In this case, the displacement will be 3 m/s * time.

To find the time it takes for the canoe to reach the dock, we need to determine the time it takes for the canoe to travel 112 meters eastward. The eastward component of the canoe's velocity is the same as the river's current, which is 7 m/s. The time can be calculated using the formula: time = displacement / velocity. In this case, the time will be 112 m / 7 m/s.

Therefore, the displacement of the canoe is 3 m/s * time and the time it takes to reach the dock is 112 m / 7 m/s. The person in the canoe would have to paddle at a velocity perpendicular to the river's current, which is 3 m/s, in order to land at the dock.