( you may assume that north is the y- direction and east the x direction for thi

Question

( you may assume that north is the y- direction and east the x direction for this question)

you are piloting a boat that moves at a constant speed of 10 km/hr relative to the water beneath it

a) on a body of still water you point your boat due north for 2 hours then turn due east and continue for another 3 hours what is your displacment vector ? and average velocity vector over this trip

b) suppose now that the water flows southward with constant speed of 5 km/hr while you attempt the same trip in part a point you rboat due north for 2 hours then turn due east for 3 hours what would your displacment vector and average velocity vector relative to earth over this trip ?

Explanation / Answer

north is the y- direction and east the x direction

Velocity of water with respect to water = 10 km / hr

a)boat due north for 2 hours i.e distance travelled = 2*10 = 20 km in north

due east for another 3 hours

Distance in this direction = 3*10 = 30 km

displacment vector = (30 i + 20 j ) km       where i and j are unit vectors in East and north direction respectevely

average velocity vector over this trip = displacement / total time = (30 i + 20 j )/ 5    = (6 i + 4 j ) km/hr     

b)

now the water flows southward with constant speed of 5 km/hr

Displacement in first 2 hrs = (10 -5 )*2 = 10 j

Displacement in next 3 hrs = 10*3 i - 5*3 j = 30 i - 15 j

So Final displacment vector = 30 i - 5 j    km

average velocity vector = displacment vector / total time = 6 i - j     km/hr

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