Physics? relative velocity?

Question

a boat can travel at a speed of 20 km/h relative to water. the boat sails across river (perpendicular to the river bank) and reaches a point 5 km directly across from its launch point. the water is flowing at a speed of 8 km/h parallel to the river bank.

a. at what angle must the boat steer to reach its destination?

b. how much time is required for the boat to make the trip?

please explain

thank you

Answer 1

Draw a triangle ABC with A and B directly opposite each other on the two river banks, and B above A in the diagram.

AB represents the resultant velocity of the boat after allowing for the current.

Draw CB at right angles to AB with C left of B to represent the 8 km/hr. river current.

AC = 20 km/hr represents the magnitude and direction of the speed of the boat relative to the water.

(a)

sin(BAC) = CB / AC = 8 / 20

Angle BAC = 23.6 deg. to the intended direction is the course the boat should steer.

(b)

The length of AB represents the resultant speed of the boat.

AB^2 = AC^2 - CB^2

= 20^2 - 8^2

AB = 18.33 km/hr.

The boat will cover the 5km distance in:

5 * 60 / 18.33 = 16.4 min.