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A sailboat is sailing due east at 8.20 mph. The wind appears to blow from the southwest at 10.9 mph. What is the true wind speed? What is the true wind speed if the wind appears to blow from the northeast at 10.9 mph?

2007-03-14 15:53:34 · 2 answers · asked by RelientKayers 4 in Science & Mathematics Physics

2 answers

1.

There are two components - one in the direction of the ship (ie, east-west) and one normal to the direction of motion of the ship (ie. north-south).

The north-south component of the wind is 10.9 sin45 = 7.707mph.

The east-west component is 8.2 + 7.707 = 15.907mph

This is because the ship and the wind are in the same direction.


2.

If the wind comes from the northeast, then the true speed of the wind is now

8.2 - 7.707 = 0.493mph

This is the east-west component and we use relative motion as the ship and the wind are in opposing directions.

The north-south component is the same as before....

2007-03-14 16:17:51 · answer #1 · answered by Alex 1 · 0 0

i,j,k are unit vectors

vs=8.2i

apparent wind speed=10.9/(√2)i+10.9/(√2)j

true wind=sailboat-apparent wind

tw=8.2i-(10.9/(√2)i+10.9/(√2)j)
reducing to numbers
0.49i-7.71j

the absolute value=√(0.49)^2+(7.71)^2)=7.73

for the other direction we have
tw=8.2i-(-10.9/(√2)i-10.9/(√2)j)
=8.2i+10.9/(√2)i+10.9/(√2)j
=19.1i+10.9j
absolute value is √(19.1^2+10.9^2)=22

2007-03-14 16:27:21 · answer #2 · answered by Rob M 4 · 0 0

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