2020-01-24T05:34:55-05:00
A kayaker is traveling down a river at 7.5 knots due south when it encounters a current that is 4.3 knots at 43° east of north what is the new speed and direction of the boat
1
2020-01-27T09:30:29-0500
v = ( 0 , 7.5 ) k n o t s \bold{v}=(0,7.5)knots v = ( 0 , 7.5 ) kn o t s
u = ( 4.3 sin 43 , − 4.3 cos 43 ) k n o t s \bold{u}=(4.3\sin{43},-4.3\cos{43})knots u = ( 4.3 sin 43 , − 4.3 cos 43 ) kn o t s
v ′ = v + u = ( 4.3 sin 43 , 7.5 − 4.3 cos 43 ) = ( 2.93 , 4.36 ) k n o t s \bold{v'={v+u}}=(4.3\sin{43},7.5-4.3\cos{43})=(2.93,4.36)knots v ′ = v + u = ( 4.3 sin 43 , 7.5 − 4.3 cos 43 ) = ( 2.93 , 4.36 ) kn o t s
v = 2.9 3 2 + 4.3 6 2 = 5.3 k n o t s v=\sqrt{2.93^2+4.36^2}=5.3\ knots v = 2.9 3 2 + 4.3 6 2 = 5.3 kn o t s The direction:
θ = arctan 2.93 4.36 = 34 ° e a s t o f s o u t h \theta=\arctan{\frac{2.93}{4.36}}=34\degree\ east\ of \ south θ = arctan 4.36 2.93 = 34° e a s t o f so u t h
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