Ricardo and Jane are standing under a tree in the middle of a pasture. An argument ensues, and they walk away in different directions. Ricardo walks 25.0 in a direction 60.0 west of north. Jane walks 14.0 in a direction 30.0 south of west. They then stop and turn to face each other.
What is the distance between them?
Express your answer with the appropriate units.
I would use the law of cosines. draw the figure, you know the angle between, and the two length.
sides: 14, 25. Angle between is 30+30
distance^2=14^2 + 25^2 -2*14*25cos60
To find the distance between Ricardo and Jane, we can use the concept of displacement. Displacement is the shortest distance between two points, which can be calculated using the Pythagorean theorem.
First, let's find the horizontal and vertical components of Ricardo's and Jane's displacements:
Ricardo's horizontal displacement (Rx) = distance * sin(angle) = 25.0 * sin(60.0) = 25.0 * 0.866 = 21.65
Ricardo's vertical displacement (Ry) = distance * cos(angle) = 25.0 * cos(60.0) = 25.0 * 0.5 = 12.5
Jane's horizontal displacement (Jx) = distance * cos(angle) = 14.0 * cos(30.0) = 14.0 * 0.866 = 12.12
Jane's vertical displacement (Jy) = distance * sin(angle) = 14.0 * sin(30.0) = 14.0 * 0.5 = 7.0
Now, we can find the total horizontal and vertical displacements between Ricardo and Jane:
Total horizontal displacement (Dx) = Rx - Jx = 21.65 - 12.12 = 9.53
Total vertical displacement (Dy) = Ry + Jy = 12.5 + 7.0 = 19.5
Finally, we can use the Pythagorean theorem to find the distance between them:
Distance = sqrt(Dx^2 + Dy^2) = sqrt(9.53^2 + 19.5^2) = sqrt(90.7009 + 380.25) = sqrt(470.9509) ≈ 21.7
Therefore, the distance between Ricardo and Jane is approximately 21.7 units (where the units depend on the original distance measurement).