Ann is driving a motorboat across a river that is 2 km wide. The boat has a speed of 20 km/h in still water, and the current in the river is ﬂowing at 5 km/h. Ann heads out from one bank of the river for a dock directly across from her on the opposite bank. She drives the boat in a direction perpendicular to the current. (a) How far downstream from the dock will Ann land? (b) How long will it take Ann to cross the river?

The resultant velocity of the motorboat due to the current perpendicular to the motion of the boat can be calculated by drawing a triangle to represent this motion. The velocity of the motorboat is the base whereas the velocity of the river is the perpendicular of the triangle (picture attached).

The angle is [tex]Tan^{-1}[/tex](perpendicular/base);

[tex]Tan^{-1}[/tex](5/20)= 14.0;

The triangle can be enlarged such that the perpendicular now represents the width of the river and the perpendicular represents the distance between the dock and landing place.

The distance between dock and landing place is:

a) base*Tan(∅) = 2*Tan(14) = 0.5km

b Time = 2/20= 0.1 hours. This is because the horizontal component of the motion due to velocity of motor boat will be considered for horizontal distance of 2 km.