An airplane is flying due East with a velocity of 166 m/s. A strong wind is blowing 145 m/s at angle of 147 degrees. What is the speed of the airplanes as a result of the wind?
To find the speed of the airplane as a result of the wind, we need to find the resultant velocity of the airplane and the wind.
First, let's separate the wind velocity into its horizontal and vertical components. The horizontal component of the wind velocity is given by:
horizontal component = wind velocity * cos(angle)
horizontal component = 145 m/s * cos(147 degrees) = -43.53 m/s
Note that we use a negative sign because the wind is blowing in the opposite direction of the airplane's motion.
Next, let's add the horizontal component of the wind velocity to the velocity of the airplane:
resultant velocity = airplane velocity + horizontal component of wind velocity
resultant velocity = 166 m/s + (-43.53 m/s)
resultant velocity = 122.47 m/s
Therefore, the speed of the airplane as a result of the wind is 122.47 m/s.