A plane is flying west at 214 km/h. The wind is blowing south at 108km/h. a what is the ground speed of the plane
b In what direction does the plane travel
and speed
the resultant vector is <-214,0> + <0,-108> = <-214,-108>
now just find the direction and magnitude of that vector.
To find the ground speed of the plane and its direction, we can use vector addition.
a) The ground speed of the plane can be found by adding the speed of the plane (westward) to the speed of the wind (southward).
Ground speed = plane speed + wind speed
Let's assign positive values to the eastward and northward directions, and negative values to the westward and southward directions.
Plane speed = -214 km/h (westward)
Wind speed = -108 km/h (southward)
Ground speed = -214 km/h + (-108 km/h)
Ground speed = -322 km/h
Therefore, the ground speed of the plane is 322 km/h.
b) To determine the direction of the plane's travel, we need to find the angle between the ground speed vector and the eastward direction.
Let's consider the eastward direction as 0 degrees.
Using trigonometry, we can find the angle using the tangent function:
angle = arctan(ground speed / wind speed)
angle = arctan(-322 km/h / -108 km/h)
angle = arctan(2.981)
Using a calculator, we find that the angle is approximately 71.89 degrees.
Since the ground speed is in the westward direction, we subtract the angle from 180 degrees:
Direction = 180 degrees - 71.89 degrees
Direction ≈ 108.11 degrees
Therefore, the plane travels in a direction approximately 108.11 degrees east of north.
To find the ground speed of the plane, we need to use vector addition.
a) The ground speed of the plane is the resultant vector of the plane's velocity and the wind's velocity.
We can use the formula for vector addition to find the ground speed:
Ground speed = √((plane's velocity)^2 + (wind's velocity)^2)
Given that the plane is flying west at 214 km/h and the wind is blowing south at 108 km/h, we can plug in these values into the formula:
Ground speed = √((214 km/h)^2 + (108 km/h)^2)
Ground speed = √(45796 km^2/h^2 + 11664 km^2/h^2)
Ground speed = √(57460 km^2/h^2)
Ground speed = 239.8 km/h (rounded to one decimal place)
So, the ground speed of the plane is approximately 239.8 km/h.
b) To determine in what direction the plane is traveling, we need to find the angle between the ground speed vector and a reference direction (usually north or east).
We can use trigonometry to find this angle.
Angle = arctan((wind's velocity)/(plane's velocity))
Given that the plane is flying west at 214 km/h and the wind is blowing south at 108 km/h, we can plug in these values into the formula:
Angle = arctan(108 km/h / 214 km/h)
Angle ≈ 26.3 degrees (rounded to one decimal place)
So, the plane is traveling approximately 26.3 degrees south of due west.