Question

The velocity of the boat with respect to the ground is 3i+4j and velocity of river with respect to ground is-3i+4j

Answer 1

The velocity of the boat, Vb = 3 i cap + 4 j cap

The velocity of the water with ground, Vm = -3 i cap + 4 j cap

Relative velocity of the boat with respect to that of water, Vbw = Vb – Vm

Vbm = 3 i cap + 4 j cap – (-3 i cap + 4 j cap)

Vbm = 3 i cap + 4 j cap + 3 i cap - 4 j cap

Vbm = 6 i cap

Answer 2

Complete Question: The velocity of the boat with respect to the ground is 3i+4j and velocity of river with respect to ground is -3i + 4j. Find relative velocity of the boat w.r.t. water.

Answer:

Relative velocity(Vbr) = 6i m/s

Explanation:

Refer to the attached image for better understanding the case.

Given;-

           Vbg = 3i + 4j  [where, Vbg is velocity of boat w.r.t. ground]

           Vr = - 3i + 4j [where, Vr is velocity of river water]

Now, finding Vbr [where, Vbr is velocity of boat w.r.t. river];-

           Vbr = Vbg - Vrg    [where, Vrg is velocity of river w.r.t. ground]

           Vbr = (3i + 4j) - (-3i + 4 j)

           Vbr = 3i + 4j + 3i - 4j

           Vbr = 6i

Therefore, the relative velocity of boat w.r.t. river is 6i m/s.