Answer: The angle of Brenda's velocity, as observed by an observer on the ground, is 76.537°.
Step-by-step explanation:
the angle of Brenda's velocity, as observed by an observer on the ground, is 76.537°.
The tangent of this angle can be calculated using the formula:
Tanθ = opposite/adjacent
where θ is the angle formed by Brenda's velocity vector and the east direction of the air velocity vector.
To use this formula, we need to find the opposite and adjacent sides of the triangle formed by Brenda's velocity vector and the east direction of the air velocity vector. Let's draw a diagram to help us visualize this situation:
the opposite side is Brenda's southward velocity component of 45.0 m/s and the adjacent side is the eastward velocity component of the air of 9.9 m/s. Therefore, the tangent of the angle θ is:
Tanθ = opposite/adjacent
= 45.0 m/s ÷ 9.9 m/s
= 4.54545...
we can find the inverse tangent of this value to get the angle θ:
Tan⁻¹(4.54545...) = 76.537°
Therefore, the angle of Brenda's velocity, as observed by an observer on the ground, is 76.537°.