A 280-m-wide river flows due east at a uniform speed of 3.5m/s. A boat with a sp

Question

A 280-m-wide river flows due east at a uniform speed of 3.5m/s. A boat with a speed of 6.6m/s relative to the water leaves the south bank pointed in a direction 32 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 4.078 Units m/s (b) Number -59.05 Units degree (degree) (c) Number 68.66 Units s

Explanation / Answer

velocity of river relative to ground Vrg = 3.5 i

velocity of boat relative to water Vbr = -6.6*sin32i + 6.6*cos32 j

velocity of boat relative to ground Vbg = Vbr + Vrg

Vbg = -6.6*cos32i + 6.6*sin32 j + 3.5 i

Vbg = -3.5i + 5.6 j + 3.5i

Vbg = 5.6 j

(a)

magnitude = 5.6 m/s

(b)

0

(c)

time = width/velocity

time = 280/5.6 = 50 s

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