Question

A section of a river is 252m wide and the water flows east with a uniform velocity of 1.10m/s. A boat starts at point A on the south bank and crosses the river to point B on the opposite side. If the trip takes 3.00min, find the velocity (magnitude and direction) of the boat with respect to

a. a stationary observer on the ground.

b. a duck floating and moving with the water.

Answer 1

Here ,

width of the river , w = 252 m

u = 1.1i m/s

time taken , t = 3 min

a) for the net velocity with respect to ground

velocity with respect to the stationary observer = W/time

velocity with respect to the stationary observer = 252/(3 * 60)

velocity with respect to the stationary observer = 1.4 m/s in north direction

the velocity with respect to the stationary observer is 1.4 m/s in north direction

b) Now, for the velocity of the boat with respect to the duck

velocity of the boat with respect to the duck = sqrt(1.4^2 + 1.1^2)

velocity of the boat with respect to the duck = 1.78 m/s

the velocity of the boat with respect to the duck is 1.78 m/s

theta = arctan(1.1/1.4) = 38.2 degree

it is 1.78 m/s at 38.2 degree north of west