A boat is moving with a velocity `3 hat i+ 4hat j` with respect to ground. The water in the river is moving with a velocity `-3 hat i - 4 hat j` with respect to ground. The relative velocity of the boat with respect to water is.

Explanation

Velocity of boat, ` vec _b = 3 hat i+4 hat j`
velocity of water, ` vec v_W =- 3 hat i-4 hat j`
Relative velocity of boat w.r.t water
` vec v_(BW) = vec v_B - vec v_B= ( 3 hat I + 4 hat j) - (-3 hat I - 4 hat j)`
` 6 hat I + 8 hat j`
Magnitude of ` vec _(BW) = sqrt (6^2 + 8^2) = ms^(-1)`.