A plane leaves Seattle, flies 79.0 at 22.0 north of east, and then changes direction to 48.0 south of east. After flying at 123 in this new direction, the pilot must make an emergency landing on a field. The Seattle airport facility dispatches a rescue crew.
In what direction should the crew fly to go directly to the field? Use components to solve this problem.
Let x be east and y be north.
The total x displacement is
x = 79 cos 22 + 123 cos 48
The total y displacement is
y = 79 sin 22 - 123 sin 48
Compute these numbers. y/x will be the tangent of the angle one must go. y will be negative, and x positive, so it will be south of east by that amount
26.7
-0.0582
Bot, Please answer this question
Find the mean absolute deviation (MAD) of the data
98 132 295 68 176 89 287 198 94 68 240 94 369 94 155
To find the direction the crew should fly to go directly to the field, we need to calculate the x and y displacements.
Let x be east and y be north.
The total x displacement can be calculated by finding the sum of the x-components of the two legs of the flight. The first leg is 79.0 at 22.0 north of east, which means the x-component is 79.0 cos 22°. The second leg is 123 in a direction 48.0 south of east, so the x-component is 123 cos 48°. Add these two components together to get the total x displacement:
x = 79.0 cos 22° + 123 cos 48°
Similarly, the total y displacement can be calculated by finding the sum of the y-components of the two legs of the flight. The first leg is 79.0 at 22.0 north of east, which means the y-component is 79.0 sin 22°. The second leg is 123 in a direction 48.0 south of east, so the y-component is -123 sin 48° (negative because it is south). Add these two components together to get the total y displacement:
y = 79.0 sin 22° - 123 sin 48°
Now we have the x and y displacements. To find the direction to go directly to the field, we need to find the angle tangent of the ratio y/x, because y/x represents the tangent of the angle one must go.
So we have the direction angle:
tan θ = y / x
Compute these numbers using a calculator or trigonometric functions to find the values of x and y, then calculate y/x. This will give you the tangent of the angle one must go.
Finally, since y is negative and x is positive, the direction will be south of east by the amount given by y/x.