You are in your kayak, paddling across the Charles river, which we can treat as

Question

You are in your kayak, paddling across the Charles river, which we can treat as having parallel banks separated by a distance of 540. m. The river is flowing east at a constant speed of 1.60 km/h, and you paddle your kayak at a constant velocity, relative to the water, of 5.80 km/h at an angle of 30.0° east of north.

(a) What is your velocity relative to a fixed point on the shore?
Your velocity relative to the shore is km/h at an angle of ° east of north.

(b) How much time, in seconds, does it take you to paddle from one bank of the river to the other, under the conditions described above? Note that you will not land on the far side at the point directly across the river from where you started.
s

(c) While you are crossing the river, how far downriver do you travel (in meters)?
m

Explanation / Answer

relative to the water you are going v*sin(30) = 2.9km/h east (X-direction) relative to the ground you are going 2.9+1.6 = 4.5km/h east or 1.25 m/s now in the north (Y-direction), you are going 4.5*cos(30) =3.897km/h so it takes you .540km/3.897km/h = .138564 hours or 498.931 seconds you are going 4.5km/h east (X-direction) so you end up 4.5km/h * .138564hours = .623538km east or 623.538m

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