What is the velocity of the airplane if the compass indicates due north, airspeed is 240 km/hr, and there is a 100 km/hr wind from west to east?
The velocity of the airplane can be calculated by considering the airspeed and the wind speed. The airplane is moving through the air at 240 km/hr due north. Meanwhile, there is a wind blowing from west to east at a speed of 100 km/hr. To find the velocity of the airplane, we need to calculate the resultant velocity, which is the vector sum of the airspeed and wind speed.
Calculating the Resultant 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.
Given that the airspeed of the airplane is 240 km/hr and the wind speed is 100 km/hr, we can represent these velocities as vectors. The airspeed vector points north with a magnitude of 240 km/hr, while the wind speed vector points east with a magnitude of 100 km/hr.
Using the Pythagorean theorem, we can find the magnitude of the resultant velocity:
\[R^2 = (240)^2 + (100)^2\]
\[R = \sqrt{57600}\]
\[R = 260 \text{ km/hr}\]
Therefore, the velocity of the airplane, taking into account both the airspeed and the wind speed, is 260 km/hr. This means that the airplane is moving northeast at an angle between north and east, with a speed of 260 km/hr.
Understanding Resultant Velocity
The resultant velocity is the combined effect of all individual velocities acting on an object. It considers both the magnitude (speed) and direction of each velocity vector.
In this scenario, the resultant velocity represents the overall motion of the airplane as it moves through the air with the influence of the wind. By calculating the resultant velocity, we can determine how fast and in which direction the airplane is actually traveling.
It is essential to consider vector addition when calculating resultant velocity, as it involves combining the magnitudes and directions of different velocities to determine the final motion of the object. In this case, the airplane's movement is determined by the combination of its airspeed and the wind speed.
By understanding the concept of resultant velocity and applying vector addition, we can accurately determine the total velocity of the airplane relative to the ground, taking into account both its airspeed and the effect of the wind.
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