On a safari, a team of naturalists sets out toward a research station located 4.1 km away in a direction 42° north of east. After traveling in a straight line for 2.6 km, they stop and discover that they have been traveling 28° north of east, because their guide misread his compass. What are the magnitude and direction (relative to due east) of the displacement vector now required to bring the team to the research station?
2007-06-01 07:36:12 · 3 answers · asked by M&M 2 in Science & Mathematics ➔ Physics
It might help to draw this on a piece of paper. Plot a point representing the start position. Plot another representing the destination (the closer you can represent the actual problem, the better, so about 4 inches away, at about a 42 degree angle). Draw a line between them. Now plot the third point, the spot they ended up in, about 2.6 inches at a 28 degree angle. Draw a line between this point and the starting point. Triangulate the greater distance (draw a horizontal line from the starting point, intersecting a vertical line from the destination) You can figure out the angles in the triangle (42, 90, and 48), and one of the sides (4.1) solve for the remaining sides to figure out the total distance east and the total distance north they would have to travel. Repeat this process for the second point (where they ended up). Subtract the distances north and east travelled from the required distances north and east. You now have the difference in both east and north vectors which they still have to travel. Make another triangle with those vectors. Draw a line to form yet another right triangle, from them. Solve for the hypotenuse. This is the distance. Now solve for the angle opposite the vertical line. This is the angle. I'll edit this to include the answers in a moment...need to work it out...
Added: If I did it all right, they need to travel 1.7 km in a direction 64 degrees north of east.
2007-06-01 07:49:51 · answer #1 · answered by Master Maverick 6 · 2⤊ 0⤋
Break the problem into x and y components
The remaining distances I will call x and y
x=4.1*cos(42)-2.6*cos(28)
y=4.1*sin(42)-2.6*sin(28)
The angle will be ATAN(y/x)
and the magnitude will be
sqrt(x^2+y^2)
j
2007-06-01 07:49:52 · answer #2 · answered by odu83 7 · 0⤊ 0⤋
Are you sure this is Physics? Physics is easy, I could work on this problem for 2 weeks and still not solve it.
2007-06-01 07:44:10 · answer #3 · answered by Mr0Whatever 2 · 0⤊ 3⤋