Assume that the water has uniform velocity, represented above by the vector labe

Question

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

CHOOSE GREATER THAN LESS THAN OR EQUAL TO from the statements below.

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

Explanation / Answer

net velocity of the boy will be

velocity of the boat+velocity of the river

now lets say, the velocity of the boat makes an angle theta will horizontal. and speed is v.

speed of river is along vertical and speed is u.

then net speed along the vertical=u+v*sin(theta)

and net speed along the horizontal is v*cos(theta)

now time taken to cross the river=width of the river/speed along horizontal

=w/(v*cos(theta))

so as v is constant, higher the value of cos(theta) i.e. lower the value of theta, the time taken to cross the river will be lower.

part 1:

for J and A theta magnitude is same and only sign is different.

as cos(theta)=cos(-theta)

they will take the same time.

part 2:

angle for A is greater than angle for C hence time for A is greater than time for C.

part 3:

angle for J is greater than angle for K hence time for J is greater than time for K.

part 4:
distance travelled across horizontal is the same for every direction.
across vertical,distance =(u+v*sin(theta))*w/(v*cos(theta))

so lower the value of theta, distance will be lower.

and as for positive theta, u+v*sin(theta) is greater than value for negative theta.

as for A, theta is positive and same in magnitude as of J.

hence distance travelled for A will be greater than J.

part 5:

higher the angle greater the speed.

so speed for A is greater than speed for C.

so answers are:

equal to
greater than
greater than
greater than
greater than

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects