A plane is headed due east with airspeed of 240 mph. if a wind at 40 mph is bloiwing from the north , find the ground speed of the plane.
To find the ground speed of the plane, we need to consider the combined effect of the plane's airspeed and the wind speed.
The airspeed of the plane is given as 240 mph, and the wind is blowing from the north at 40 mph. Since the plane is heading due east, the wind is perpendicular to its direction.
We can use vector addition to find the resultant velocity, which represents the ground speed of the plane. The resultant velocity is the sum of the plane's airspeed and the wind velocity.
To calculate the resultant velocity, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
In this case, the plane's airspeed and the wind velocities are the two sides of the right triangle, and the resultant velocity is the hypotenuse.
Let's calculate the ground speed:
1. The plane's airspeed is 240 mph, which represents the eastward component.
2. The wind speed is 40 mph, which represents the northward component.
3. Using the Pythagorean theorem, we can calculate the magnitude of the resultant velocity (the hypotenuse):
Ground speed = sqrt(airspeed^2 + wind speed^2)
= sqrt(240^2 + 40^2)
= sqrt(57600 + 1600)
= sqrt(59200)
≈ 243.08 mph
Therefore, the ground speed of the plane is approximately 243.08 mph.