Final answer:
To find the speed and direction of the wind as observed by a stationary observer when a cyclist is traveling southeast along a road and there is a wind blowing from the southwest, we can use vector addition. By breaking down the velocities of the cyclist and the wind into their components and adding them together, we can determine that the speed of the wind is 15 km/h in the direction of 135°.
Step-by-step explanation:
The question is asking for the speed and direction of the wind as observed by a stationary observer when a cyclist is traveling southeast along a road at 15 km/h and there is a wind blowing from the southwest at 25 km/h. To calculate the speed and direction of the wind, we can use vector addition. The velocity of the cyclist is given as 15 km/h in the southeast direction. The velocity of the wind is given as 25 km/h in the southwest direction. To find the speed and direction of the wind, we need to add the velocities of the cyclist and the wind.
We can represent the velocity vectors as follows:
Velocity of cyclist = 15 km/h (southeast)
Velocity of wind = 25 km/h (southwest)
To add these vectors, we can break them down into their components:
Velocity of cyclist = 15 km/h * sin(45°) (south) + 15 km/h * cos(45°) (east)
Velocity of wind = 25 km/h * sin(225°) (south) + 25 km/h * cos(225°) (west)
Adding the components of the velocities:
Velocity of cyclist + Velocity of wind = (15 km/h * sin(45°) + 25 km/h * sin(225°)) (south) + (15 km/h * cos(45°) + 25 km/h * cos(225°)) (east)
Calculating the components:
Velocity of cyclist + Velocity of wind = (-10.61 km/h) (south) + (-10.61 km/h) (east)
To find the speed and direction of the wind, we can use the Pythagorean theorem and trigonometry:
Speed of wind = sqrt((-10.61 km/h)^2 + (-10.61 km/h)^2) = 15 km/h
Direction of wind = atan2((-10.61 km/h), (-10.61 km/h)) = 135°
Therefore, the speed of the wind as observed by the stationary observer is 15 km/h in the direction of 135°.