Aircraft approaching landing, vector, velocity, position problem. Help

[raven2783]

Homework Statement

As an aircraft approaches landing, the components of its position are given by:

x=81t y=500-27t

Velocity vector of aircraft during descent is given by:

81m/s (i hat) + -27m/s (j hat)

The value of the speed during the descent is:

85.381m/s

What angle does the velocity vector make with the horizonal?

2. The attempt at a solution

I tried the Law of Sines sin90/85.381=sina/-27 and sin90/85.381=sina/81 but the angles of this triangle other then 90 are not what they are looking for. What do they mean horizontal?? help!

 

[buffordboy23]

The horizontal would be your x-axis; in this case, the runway. Draw the velocity component vectors on an xy-axis. Now draw your resultant vector (the hypotenuse), which you are trying to determine the angle of. What trigonometric relation will give you this angle?

See link for formulas:

http://en.wikipedia.org/wiki/Trigonometry#Overview

 

[baba89]

Based on the given information, it seems that the angle they are looking for is the angle between the velocity vector and the horizontal axis. To find this angle, you can use the trigonometric function "arctan" (or "tan^-1") which is the inverse of "tan" and can be found on most scientific calculators.

Using this function, you can calculate the angle by taking the inverse tangent of the vertical component of the velocity vector (-27) divided by the horizontal component (81). This will give you an angle of approximately -19.5 degrees. However, since this angle is measured from the negative x-axis, you can add 180 degrees to get the angle measured from the positive x-axis, which would be approximately 160.5 degrees.

So, the angle that the velocity vector makes with the horizontal axis is approximately 160.5 degrees.