Sarah can paddle a rowboat at 6 m/s in still water. She heads out across a 400 m river at an angle of 30 upstream. She reaches the other bank of the river 200 m downstream from the direct opposite point from where she started. Determine the river current?

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Menziani8o2 · Accepted Answer

Let us consider this as a projectile problem where there is no acceleration.Let             v      R       be river current. Sarah&#039;s motion has two components.Across the river.Along the river.Both can be handled separately because they are orthogonal to one another. Given is width of river       =    400         m  200 meters downstream from the opposite point of start is the place of landing on the other bank.We know that time taken to paddle directly across must be equal to time taken to travel       200         m   downstream parallel to the current. Let it be equal to       t  Setting up equation across the river            (      6              cos        30            )        t    =    400        ⇒    t    =          400              6                  cos          30                    ......(1)She paddles upstream with the current in equation            (              v        R            -      6              sin        30            )        t    =    200   .....(2)Using (1) to rewrite (2) we get            (              v        R            -      6              sin        30            )        ×          400              6                  cos          30                      =    200        ⇒          v      R        =          200      400        ×          (      6              cos        30            )        +    6          sin      30            ⇒          v      R        =    2.6    +    3        ⇒          v      R        =    5.6         m          s              -        1

Sarah can paddle a rowboat at 6 m/s in still water. She heads out across a 400 m river at an angle of 30 upstream. She reaches the other bank of the river 200 m downstream from the direct opposite point from where she started. Determine the river current?

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