A plane is travelling 20km/hr heading north while the wind velocity is 60km/hr north 30 degrees east, what is the distance travelling by the plane after 2 hrs
I quess you mean the direction the wind is going instead of where it is coming from. If not reverse the wind components I use.
Vnorth = 20 + 60 cos 30 = 72
Veast = 60 sin 30 =30
speed = sqrt (72^2 + 30^2) = sqrt (6084) = 78
78 * 2 = 156 km
To determine the distance traveled by the plane after 2 hours, we need to calculate the resultant velocity of the plane by considering its own velocity and the wind velocity.
First, let's break down the wind velocity into its north and east components. The wind is traveling north 30 degrees east, so we can calculate the north and east components using trigonometry.
The north component of the wind velocity can be found using the formula: north component = wind velocity * cos(angle).
The east component of the wind velocity can be found using the formula: east component = wind velocity * sin(angle).
Plugging in the values, we get:
north component = 60 km/hr * cos(30 degrees) = 60 km/hr * √(3)/2 = 30√(3) km/hr (approx. 51.96 km/hr)
east component = 60 km/hr * sin(30 degrees) = 60 km/hr * 1/2 = 30 km/hr
Now, let's calculate the resultant north component of the plane's velocity by adding its own north velocity to the north component of the wind velocity:
Resultant north component = plane's north velocity + north component of wind velocity.
Since the plane is moving at a constant speed of 20 km/hr north, the resultant north component of the plane's velocity is:
Resultant north component = 20 km/hr + 30√(3) km/hr (approx. 51.96 km/hr)
Next, let's calculate the resultant east component of the plane's velocity by adding its own east velocity to the east component of the wind velocity:
Resultant east component = plane's east velocity + east component of wind velocity.
Since the plane is not moving in the east direction (it is only moving north), the resultant east component of the plane's velocity is:
Resultant east component = 0 km/hr + 30 km/hr = 30 km/hr.
Now that we have the north and east components of the resultant velocity vector, we can calculate the magnitude (speed) and direction of the resultant velocity.
The magnitude of the resultant velocity can be found using the Pythagorean theorem:
Resultant velocity = √(north component^2 + east component^2).
Plugging in the values, we get:
Resultant velocity = √((51.96 km/hr)^2 + (30 km/hr)^2) = √(2700 + 900) km/hr ≈ √(3600) km/hr = 60 km/hr.
Therefore, the magnitude of the resultant velocity (speed of the plane) is 60 km/hr.
Finally, we can calculate the distance traveled by the plane after 2 hours using the formula: distance = speed * time.
Plugging in the values, we get:
Distance traveled = 60 km/hr * 2 hr = 120 km.
Therefore, the plane will travel 120 kilometers after 2 hours.