Question

A person is riding in a hot air balloon. For the first hour, the wind current is a constant 8.25 mph in the direction N37.5°E. Then the wind current changes to 6.00 mph and heads the balloon in the direction S52.5°E. What is the bearing of the balloon from its starting point? Round your answer to 1 decimal place.

Answer 1

Answer:

The bearing of the balloon from its starting point = N 71.9° E

Step-by-step explanation:

To find the distance to the starting point, the wind and the height are perpendicular to each other. So, use the Pythagorean Theorem :

(Distance from the starting point)² = 8.25² + 6.00² = 112.56

⇒ Distance = 10.6 miles

Then to determine the bearing y :

$\tan x=\frac{ opposite}{adjacent}\\\\Therefore, \tan x = \frac{6}{8.25} = 0.6857\\\\\implies x = \tan^{-1} (0.6857) ={34.4}^{\circ}$

Since the original bearing that the balloon set off at was N 37.5° E,  

⇒  y = 37.5° + 34.4°

       = 71.9°

Hence, The bearing of the balloon from its starting point = N 71.9° E