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Point A is located on the western bank of a river, and point C is located directly across stream on the eastern bank. The river is 648.6 m wide and flows due south at 2.54 km/hr. A boat wants to cross the river from point A to point C. Determine the bearing and velocity that must be maintained by the boat in order to arrive at point C in 10 minutes.

Respuesta :

Answer:

1.29 m/s ∠ 35.2°

Explanation:

Let consider point A and C are in horizontal direction and the stream flows in vertical direction.

Horizontal Velocity:

The boat has to cross the river in 10 minutes and reach point C.

so Vi= 648.6/(10*60) m/s

Vi=1.08 m/s

Vertical Velocity:

The water will flow the boat in south direction, to reach point C the boat need to acquire same velocity in the opposite direction of river flow.

so

Vj= (2.54 km)/(1 hr) = (2.54*1000 m)/3600 sec

Vj= 0.706 m/s

Magnitude of Velocity:

V=[tex]\sqrt{vi^{2}  +vj^{2} }[/tex]

V= [tex]\sqrt{(1.08)^{2}+(0.706)^{2} } }[/tex]

V=1.29 m/s

Direction of boat:

∅=[tex]tan^{-1 } (vj/vx)[/tex]

∅=[tex]tan^{-1 } (0.706/1.08)[/tex]

∅=35.2°

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