How Do You Calculate a Boat's Path Across a River with a Current?

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To calculate a boat's path across a river with a current, first determine the boat's speed relative to the starting point by using vector addition of the boat's speed in still water and the current's speed. The time taken to cross the river can be calculated by dividing the river's width by the component of the boat's speed directed across the river. Additionally, the downstream distance can be found by calculating how far the current carries the boat during the crossing time. A right triangle can be used to visualize the relationship between the boat's speed and the current. Understanding these components is crucial for solving the problem effectively.
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1. A boat has a speed of 1.50 ms-1 in still water. It is used to cross a river 500 m wide along which there is a strong current of speed 0.900 ms-1. The boat is directed straight towards the opposite bank but the water current carries it downstream. Calculate:
(A) the boat's speed relative to the starting point
(B) the time taken to reach the bank on the other side
(C) the distance the boat is carried downstream from the point of departure at one bank to the point of arrival on the opposite bank



2. Literally don't know where to start. I feel like I have been staring at problems from my lectures and don't know how to relate this to any of them.



3. I drew out a diagram and can see that it makes a right triangle, but it feels like I need more information and I don't know how to find it. Also, I can't figure out how to the speed of the boat to the speed of the current.
 
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