You are riding in a boat whose speed relative to thewater is 5.2 m/s. The boat p

Question

You are riding in a boat whose speed relative to thewater is 5.2 m/s. The boat points at an angle of 25 degreesupstream on a river flowing at 1.3 m/s.             (a)What heading must the boat have if it is to land directly acrossthe river from its starting point?   degrees                (b)How much time is required for this trip if the river is 24.6 mwide? seconds You are riding in a boat whose speed relative to thewater is 5.2 m/s. The boat points at an angle of 25 degreesupstream on a river flowing at 1.3 m/s.             (a)What heading must the boat have if it is to land directly acrossthe river from its starting point?   degrees                (b)How much time is required for this trip if the river is 24.6 mwide? seconds

Explanation / Answer

if X be the direction of flow of the stream and Y along thewidth of the river            if be the starting angle of the boat with the streamvelocity direction to reach    directly across theriver from its starting point     netvelocity of the boat along x - axis               Vx = Vstream + Vcos                 Vy= Vsin    distance travelled across theriver = W = width of the river                   Vy = W / t               Vsin = W/t........eq1 and distance travelled alon x= direction = 0                 Vx = Vstream + Vcos = 0                  -Vstream = Vcos.........eq2            using this relation we can solve for angle                 =cos-1[-Vstream / V]            frm abv relations eq1 and eq2                 tan = -W / Vstream *t frm the value of determined , we can solve for time to reach other end of thestream.

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