You fly 32.0 km in a straight line in still air in the direction 35.0 degree south of west. Find the distance you would have to fly straight south and then straight west to arrive at the same point.
nknol
To find the distance you would have to fly straight south and then straight west to arrive at the same point, you can break down the given flight into its north and west components.
First, calculate the north component of the flight using the formula:
North Component = Distance × sin(θ)
where:
- Distance is the given flight distance (32.0 km)
- θ is the angle south of west (35.0°)
North Component = 32.0 km × sin(35.0°)
Now, calculate the west component of the flight using the formula:
West Component = Distance × cos(θ)
West Component = 32.0 km × cos(35.0°)
Once you have the north and west components, you can find the total distance you would have to fly straight south and then straight west by using the Pythagorean theorem:
Total Distance = √(North Component² + West Component²)
Plugging in the calculated north and west components into the equation:
Total Distance = √((32.0 km × sin(35.0°))² + (32.0 km × cos(35.0°))²)
Solving this equation will give you the answer, which is the distance you would have to fly straight south and then straight west to arrive at the same point.