Two boats, each capable of moving in still water at a constant velocity v = 6 m/

Question

Two boats, each capable of moving in still water at a constant velocity v = 6 m/s, set out to cross a river of width W = 20 m. Boat 1 heads directly across the river while boat 2 is pointed at an angle q = 60 degrees with respect to the shore as shown in the diagram below. The current in the river moves at speed v0 = 2 m/s as shown. The next two questions pertain to this situation.

4)   Which boat takes the least amount of time to cross the river?

Boat 1 takes the least time.

Boat 2 takes the least time.

Each boat takes the same amount of time.

5)  Which boat moves with the greater speed with respect to the shore?

Boat 1 moves with the greater speed with respect to the shore.

Boat 2 moves with the greater speed with respect to the shore.

Explanation / Answer

#4)

for boat (1)

v1y = v

v1x = 0

time taken t1 = distance /speed = w/v1y = w/v = 20/6 = 10/3 = 3.33 s

for boat 2

V2x = v*cos60 = v/2 = 3 m/s

v2y = v*sin60 = v*sqrt(3)/2 = 5.196 m/s

time taken , t2= W/v2y = 20/5.196 = 3.85 s

t1 < t2

Boat 1 takes the least time <---answer

+++++++++++++++++

#5)

for boat 1

reletive velocity with respect to shore

Vbs = Vbr + vrs = v1y + vox = 6i + 2j

speed = magnitude = sqrt(v1y^2 + vo^2) = 6.32 m/s   <---answer

for boat 2

ralative velocity of boat2 with respec to shore

Vbs = Vbr + Vrs

Vbr = v2x + v2y + vox = (v2x+vox) + v2y = (3+2)i + 5.196j =
5i + 5.196j

speed = sqrt(5^2 + 5.196^2) = 7.21 m/s <---answer

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