A 200-m-wide river flows due east at a uniform speed of 4.5m/s. A boat with a sp

Question

A 200-m-wide river flows due east at a uniform speed of 4.5m/s. A boat with a speed of 9.0m/s relative to the water leaves the south bank pointed in a direction 28o west of north. What is the (a) magnitude and (b) direction of the boat's velocity relative to the ground? Give the direction as the angle of the velocity from due north, positive if to the east and negative if to the west. (c) How long does it take for the boat to cross the river? A 200-m-wide river flows due east at a uniform speed of 4.5m/s. A boat with a speed of 9.0m/s relative to the water leaves the south bank pointed in a direction 28o west of north. What is the (a) magnitude and (b) direction of the boat's velocity relative to the ground? Give the direction as the angle of the velocity from due north, positive if to the east and negative if to the west. (c) How long does it take for the boat to cross the river?

Explanation / Answer

Vx = 4.5 - 9 sin 28 =0.27475593492m/s
Vy = 7.8 cos 39 = 7.94652833573m/s

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(a) The speed of the boat = magnitude of its velocity

V = sqrt ((Vx)^2 + (Vy)^2)

= 7.95127490913m/s

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(b) The angle from due north can be obtained with the function Arctan

Arctan (V_x / V_y)

= 1.97493401088deg

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(c) The time it takes to cross the river is the time is takes the coordinate y to increase by L = 200 m

t = L / V_y

= 200/ 7.94=25.1889168766 s

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