A current of a river flows steadily from west to east at 1.00 m/s. A boat in the river travels at 3.00 m/s relative to the water. The river is 20.0 m wide with parallel banks. The boat leaves the shore at point A, and point B is directly across the river from that point.

1) At what angle with respect to the north-south direction should the boat head to go directly to point B?

2) If the boat heads as in part (a), how long (in s) will it take it to reach point B?

3) Suppose the boat's motor is low on gas, so that the person guiding it wants to get to the opposite bank as quickly as possible and does not care where the boat lands. In what direction (to the north-south) should this person steer the boat?

4) Where will it land relative to B? (how many m to the east?)

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To determine the answers to these questions, we need to consider the vector addition of the boat's velocity and the river's velocity. Here's how we can solve each part of the problem:

1) To determine the angle with respect to the north-south direction, we can use trigonometry. Let's call the angle θ. Since the river flows from west to east, the angle formed between the river and the north-south direction is 90 degrees. The boat's velocity relative to the water is 3.00 m/s. To find θ, we can use the tangent function: tan(θ) = 1.00 m/s / 3.00 m/s. Taking the inverse tangent of both sides, we find that θ ≈ 18.4 degrees.

2) To find the time it takes for the boat to reach point B, we need to determine the distance the boat needs to cover. The river is 20.0 m wide, so the boat needs to travel 20.0 m to reach point B. Since the boat's velocity relative to the water is 3.00 m/s, the time it takes to travel this distance is given by t = d / v, where d is the distance and v is the velocity. Substituting the values into the formula, we get t = 20.0 m / 3.00 m/s ≈ 6.67 s.

3) If the person wants to reach the opposite bank as quickly as possible and doesn't care where the boat lands, they should steer the boat perpendicular to the river's flow. Since the river flows from west to east, the person should steer the boat directly north or south.

4) If the person steers the boat directly north or south, the boat will experience no drift due to the current because it is perpendicular to the river's flow. Therefore, the boat will land directly across from its starting point, B. There will be no eastward or westward displacement, so the boat will land exactly 20.0 m east of point B.