Ariver flows due east at 1.60 m/s. a boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.3 m/s due north relative to the water.
a) what is the velocity of the boat relative to shore?
b) if the river is 300 m wide, how far downstream has the boat moved by the time it reaches the north shore?

part (a) towards north east direction.

part (b) s = 46.60 m

Explanation:

Given,

part (a)

River is flowing due to east and the boat is moving in the north, therefore both the velocities are perpendicular to each other and,

Hence the resultant velocity i,e, the velocity of the boat relative to the shore is in the North east direction. velocities are the vector quantities, Hence the resultant velocity is the vector addition of these two velocities and the angle between both the velocities are

Let 'v' be the velocity of the boat relative to the shore.

Let be the angle of the velocity of the boat relative to the shore with the horizontal axis.

Direction of the velocity of the boat relative to the shore.

part (b)

total distance traveled in the north direction by the boat is equal to the product of the velocity of the boat in north direction and total time taken

Let 't' be the total time taken by the boat to cross the width of the river.

Therefore the total distance traveled in the direction of downstream by the boat is equal to the product of the total time taken and the velocity of the river