Question

The velocity of the current in a river is C = 0.6i + 0.8j km/hr. A boat moves relative to the water with velocity v=7i km/hr. a. What is the speed of the boat relative to the riverbed? b. What angle does the velocity of the boat relative to the riverbed make with the vector v? c. What does the angle from part b tell us in practical terms?

Answer 1

velocity of boat relative river (v) = velocity of boat relative river bed (vrb) - velocity of river (vr).
so velocity of boat relative river bed = vrb = 7i+0.6i+0.8j km/hr = 7.6i+0.8j km/hr
a) speed relative to river bed =√(7.6² + 0.8²) = 7.642 km/ph

b) angle of vrb with v is cos θ = vrb.v/(|vrb|*|v|)     [vrb.v is the dot product]

cosθ = 7.6*7/(7.642*7) = 0.9945

so θ = 6⁰

c) as θ is very small, we can say that effect of motion of river is very small. it just causes a little drift from the original direction.