relative motion

Question 1

relative motion

Answer 1

If both objects A and B move along parallel straight
lines in the opposite direction, then relative velocity of B w.r.t. A is given as,
V(ba)=V(b)-(-V(a))=V(b)+V(a)
If both objects A and B move along parallel staight lines in the same direction, then
V(ab)=V(b)-V(a)

Question 2

crossing the river

Answer 2

Case II Crossing the River To cross the river over shortest distance, i.e. to cross the river straight, the man should swim upstream making an angle θ with OB such that, OB gives the direction of resultant velocity vmR of velocity of swimmer vM and velocity of river water vR as shown in figure. Let us consider

sinθ=Vr/Vm, Vmr=√Vm^2-Vr^2
time taken to cross the river=t1=d/Vmr

Question 3

cross the river in shortest time

Answer 3

The man should go along OA. Now, the swimmer will be going along OB, which is the direction of resultant velocity vmR of vm and vR

tanθ=Vr/Vm
Vmr=√Vm^2+Vr^2
time crossing the river =t=d/Vm

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