A duck swims at 0.5 m/s West on the water of a river which is ?owing E45(degrees

Question

A duck swims at 0.5 m/s West on the water of a river which is ?owing E45(degrees)N at 2 m/s. Find the actual speed and direction of the duck by a)Resolving in the Easterly and Northern directions b)By resolving in the direction E45N and E45S For this problem still give the direction as a compass reading as in part (a). This problem is to remind you that we are not bound to take horizontal-vertical,xy,N-E etc as our choice of direction in which to resolve vectors. In fact we do not have to resolve the vector equation in two directions at right angles if we choose not to.

Explanation / Answer

1) east components: -0.5m/s + 2m/s * cos45 = 0.91 m/s north components: 2m/s * sin45 = 1.41 m/s R = sqrt(0.91² + 1.41²) m/s = 1.7 m/s T = arctan(1.41/0.91) = 57 degrees North of East, or E33N 2) They both started at point O. 4) horizontal component: 3km * cos45 = 2.12 km vertical component: 3km * sin45 - 0.1km = 2.02 km T = arctan(2.02/2.12) = 44 degrees UP from O to P R = sqrt(2.02² + 2.12²) = 2.9 km

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