A river 1 km wide has a current of velocity 4 km/h flowing from left to right.
In what direction, relative to the river bank, must a launch moving at 8 km/h steer in order to land directly opposite the starting point? How much time would this crossing take?
The river that is 1 km wide has a current with a velocity 4 km/h flowing from left to right. A launch starts from one side of the river and has to reach the point on the other side exactly opposite to this point. For this to happen, let the the direction at which the launch must travel be at an angle A to the right of the perpendicular line joining the two sides.
The final velocity of the launch should not have a component in the left to right direction. As the launch moves at 8 km/h, the component 8*sin A = 4 is in the direction opposite to that of the river.
8*sin A = 4
=> sin A = 1/2
=> A = 45 degrees
The launch must move in a direction making an angle of 45 degrees to the left of the perpendicular line joining the two sides.
The time taken by the launch in crossing the river is 1/4 = 0.25 h.