A 120-m-wide river flows due east at a uniform speed of 2.0m/s. A boat with a sp

Question

A 120-m-wide river flows due east at a uniform speed of 2.0m/s. A boat with a speed of 7.7m/s relative to the water leaves the south bank pointed in a direction 39 degree 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) Number 4.61576898921 Units m/s (b) Number -219 Units degree (degrees) (c) Number 33.453 Units 5

Explanation / Answer

here,

speed of river , vr = 2 m/s i

speed of boat , vb = 7.7 * ( - sin(39) i +cos(39) j )

vb = -4.85 i m/s + 5.98 j m/s

speed of boat relative to ground , v = vr + vb

v = - 2.85 i m/s + 5.98 j m/s

a)

the magnitude , |v| = sqrt(2.85^2 + 5.98^2) = 6.62 m/s

b)

theta = arctan(5.98/2.85)

theta = 64.5 degree north of west

c)

time taken to cross the river , t = 120 /5.98 = 20.1 s

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