You are riding on a jet ski directed at an angle upstream on a river flowing wit

Question

You are riding on a jet ski directed at an angle upstream on a river flowing with a speed of 2.8 m/s. If your velocity relative to the ground is 9.1 m/s at an angle of 25.5° upstream, what is the speed of the jet ski relative to the water?

Explanation / Answer

let us have two components of velocities 1)one along the direction of stream(i) 2)another perpendicular to the direction of stream(j) ==>speed of water stream (u)=(2.8 i) m/s given jet velocity relative to the ground is 9.1 m/s at an angle of 25.5° upstream ==>speed of jet (v) along the direction of stream = 9.1cos25.5=(8.21 i) m/s speed of jet (v) erpendicular to the direction of stream=9.1sin25.5=(3.91 j) m/s ==> speed of jet(v)=(8.21 i +3.91 j) m/s speed of the jet ski relative to the water=v-u =(8.21 i +3.91 j) -(2.8 i) =(5.41 i +3.91 j) m/s magnitude =sqroot(5.41^2+3.91^2) =6.675 m/s direction=tan^-1(3.91-5.41)=35.8 deg angle with the upstream

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