Question

A river is to be crossed by a girl using a row boat.

Rowing Speed Direction River Velocity

Assume that the water has uniform velocity, represented above by the vector labeled H. The rowing speed of the girl and a set of possible orientation of her boat are also shown. Select the direction (i.e., F, or D, or ...) in order to cross the river in the shortest time. (Notice that the number of tries is reduced.)

For which rowing orientation will the girl land on the opposite shore directly across from her starting position, neither upstream or downstream? (Notice that the number of tries is reduced.)

Select an answer for each .... below.
Greater than Less than Equal to  Time to row across for K is .... for F.
Greater than Less than Equal to  Time to row across for K is .... for D.
Greater than Less than Equal to  Time to row across for J is .... for F.
Greater than Less than Equal to  The distance traveled in crossing for A is .... for B.
Greater than Less than Equal to  For an observer on shore, the speed of the boat for C is .... for A.

Answer 1

D

By following path D, she will swim directly opposite and in the shortest time(because she will travel shortest distance)

Reason: River has speed of 2 units up. If the girl swims along D, she will have speed 2 units down, hence she will cancel the river velocity.

Select an answer for each .... below.
Greater than Less than Equal to  Time to row across for K is  equal for F. Because same horizontal component
Greater than Less than Equal to  Time to row across for K is greater than for D. Becaus hc is shorter for K
Greater than Less than Equal to  Time to row across for J is less than that for F. Vice versa
Greater than Less than Equal to  The distance traveled in crossing for A is equal for B.
Greater than Less than Equal to  For an observer on shore, the speed of the boat for C is lesser for A. Because smaller resultant formed with C