A plane is flying south at 155 km/hr and encounters a wind from the east at 60.0 km/hr. What is the plane’s new velocity with respect to the ground in standard position? The plane is flying at
To find the plane's new velocity with respect to the ground, we can use vector addition. Let's break down the velocities into their components.
The plane is flying south at a speed of 155 km/hr. Therefore, its velocity in the south direction would be 155 km/hr.
The wind is coming from the east at a speed of 60.0 km/hr. Therefore, its velocity in the east direction would be 60.0 km/hr.
To find the resultant velocity, we need to add these two vectors together. Since the plane is flying south and the wind is coming from the east, the wind will have an opposing effect on the plane's velocity.
Using the Pythagorean theorem, we can determine the magnitude of the resultant vector:
Resultant velocity magnitude = √(155^2 + 60^2)
Resultant velocity magnitude = √(24025 + 3600)
Resultant velocity magnitude = √27625
Resultant velocity magnitude ≈ 166.22 km/hr
Now, to determine the direction of the resultant velocity, we can use trigonometry. The angle between the south direction and the resultant vector can be found using the inverse tangent function:
Angle = arctan(60/155)
Angle ≈ 21.32 degrees
Therefore, the plane's new velocity with respect to the ground is approximately 166.22 km/hr at an angle of 21.32 degrees south of east.