EXAMPLE 3-10 Heading upstream. A boat's speed in still water is vgw = 1.85 m/s. If the boat is to travel north directly across a river whose westward current has speed vws = 1.20 m/s, at what upstream angle must the boat head? (See Fig. 3–29.) APPROACH If the boat heads straight across the river, the current will drag the boat downstream (westward). To overcome the river's current, the boat must have an upstream (eastward) component of velocity as well as a cross-stream (northward) component. Figure 3–29 has been drawn with vgs, the velocity of the Boat relative to the Shore, pointing directly across the river because this is where the boat is supposed to go. (Note that ves = ¥gw + Vws.) SOLUTION Vector vgw points upstream at angle 0 as shown. From the diagram, Vws 1.20 m/s sin 0 = 0.6486. VBW 1.85 m/s Thus 0 = 40.4°, so the boat must head upstream at a 40.4° angle.

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Chapter1: Units, Trigonometry. And Vectors
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 (II) Determine the speed of the boat with respect to the
shore in Example 3–10.

EXAMPLE 3-10 Heading upstream. A boat's speed in still water is vgw =
1.85 m/s. If the boat is to travel north directly across a river whose westward current has
speed vws = 1.20 m/s, at what upstream angle must the boat head? (See Fig. 3–29.)
APPROACH If the boat heads straight across the river, the current will drag
the boat downstream (westward). To overcome the river's current, the boat
must have an upstream (eastward) component of velocity as well as a cross-stream
(northward) component. Figure 3–29 has been drawn with vgs, the velocity of
the Boat relative to the Shore, pointing directly across the river because this is
where the boat is supposed to go. (Note that ves = ¥gw + Vws.)
SOLUTION Vector vgw points upstream at angle 0 as shown. From the diagram,
Vws
1.20 m/s
sin 0 =
0.6486.
VBW
1.85 m/s
Thus 0 = 40.4°, so the boat must head upstream at a 40.4° angle.
Transcribed Image Text:EXAMPLE 3-10 Heading upstream. A boat's speed in still water is vgw = 1.85 m/s. If the boat is to travel north directly across a river whose westward current has speed vws = 1.20 m/s, at what upstream angle must the boat head? (See Fig. 3–29.) APPROACH If the boat heads straight across the river, the current will drag the boat downstream (westward). To overcome the river's current, the boat must have an upstream (eastward) component of velocity as well as a cross-stream (northward) component. Figure 3–29 has been drawn with vgs, the velocity of the Boat relative to the Shore, pointing directly across the river because this is where the boat is supposed to go. (Note that ves = ¥gw + Vws.) SOLUTION Vector vgw points upstream at angle 0 as shown. From the diagram, Vws 1.20 m/s sin 0 = 0.6486. VBW 1.85 m/s Thus 0 = 40.4°, so the boat must head upstream at a 40.4° angle.
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