An airplane flies at 500km/hr, there is a wind kf 50.0km/h(N).if the pilot wants to fly due east, calculate the direction that the plane is heading.
Thanks.
Vp + 50i = 500[0o].
Vp = 500 - 50i = 503 km/h[-5.71o] = 5.71o S. of E. = Direction.
To calculate the direction that the plane is heading, you need to consider the effect of the wind on the plane's flight path.
Given:
Airplane speed = 500 km/h
Wind speed = 50.0 km/h (North)
Since the wind is blowing in a northerly direction, it will push the plane slightly off course. The resulting direction of the plane's heading is known as the "heading relative to the ground."
To find the heading relative to the ground, you can use vector addition.
1. First, draw a diagram to represent the situation. Use a scale where 1 cm represents 100 km/h. Draw an arrow to represent the airplane's velocity (500 km/h) in the easterly direction. Label this arrow "airplane velocity."
2. Next, draw another arrow to represent the wind's velocity (50 km/h) in the northerly direction. Label this arrow "wind velocity."
3. To find the heading relative to the ground, add the two vectors by placing the tail of the wind velocity vector at the head of the airplane velocity vector. The resultant vector represents the heading relative to the ground.
4. Measure the angle between the direction of the airplane velocity vector and the resultant vector. This angle represents the direction that the plane is heading relative to true north.
5. Use a protractor to measure the angle. Let's assume the angle measures 20 degrees clockwise from east.
Therefore, the direction that the plane is heading is 20 degrees east of due north.
To calculate the direction that the plane is heading, we need to take into account both the speed of the plane and the wind speed and direction.
First, let's represent the speed of the plane as 500 km/h due east. This means the plane is flying directly east at a speed of 500 km/h relative to the ground.
Next, we'll represent the wind speed as 50.0 km/h blowing from the north. The wind is blowing from the north to the south, perpendicular to the direction the plane is flying.
To calculate the resulting direction of the plane, we need to consider the vector addition of the plane's velocity and the wind's velocity. Since the wind is perpendicular to the plane's direction, we can use the Pythagorean theorem to calculate the resultant speed and direction.
We can create a right-angled triangle with the plane's velocity, the wind's velocity, and the resultant velocity as the hypotenuse. The length of the plane's velocity side is 500 km/h, and the length of the wind's velocity side is 50.0 km/h.
Using the Pythagorean theorem, we can calculate the resultant speed:
Resultant speed = √(plane's velocity^2 + wind's velocity^2)
= √(500^2 + 50^2)
= √(250000 + 2500)
= √252500
≈ 502.5 km/h
Now that we have the resultant speed, we can find the direction of the plane. The direction can be calculated using trigonometry. Since the wind is coming from the north, the angle between the plane's direction and the wind's direction is 90 degrees.
Using the tangent function:
Tangent(angle) = opposite/adjacent
In this case, the opposite side is the wind's velocity (50.0 km/h) and the adjacent side is the plane's velocity (500 km/h).
Tangent(angle) = opposite/adjacent
Tangent(angle) = 50.0/500
Tangent(angle) = 0.1
To find the angle, we can take the inverse tangent (arctan) of 0.1.
Angle = arctan(0.1)
Angle ≈ 5.71 degrees
Therefore, the direction that the plane is heading, taking into account the wind, is approximately 5.71 degrees east of due east.