An airplane was moving 50 m/s to the north relative to the air at landing. The wind was blowing 5 m/s toward the south relative to the ground. What was the speed of the airplane relative to the ground at the time of landing?
To find the speed of the airplane relative to the ground, we need to add the velocities of the airplane relative to the air and the wind relative to the ground.
The speed of the airplane relative to the ground is given by:
airplane speed relative to the ground = airplane speed relative to the air + wind speed relative to the ground.
Given that the airplane speed relative to the air is 50 m/s to the north, and the wind speed relative to the ground is 5 m/s toward the south, we can solve for the airplane speed relative to the ground.
airplane speed relative to the ground = 50 m/s + (-5 m/s) = 45 m/s.
Therefore, the speed of the airplane relative to the ground at the time of landing is 45 m/s.
To determine the speed of the airplane relative to the ground at the time of landing, we need to consider the effect of the wind. The speed of the airplane relative to the ground can be calculated by adding the velocity of the airplane relative to the air and the velocity of the wind relative to the ground.
Given:
Velocity of the airplane relative to the air (Va) = 50 m/s to the north
Velocity of the wind relative to the ground (Vw) = 5 m/s toward the south
Since the wind is blowing toward the south, its velocity can be considered as negative.
Therefore, the speed of the airplane relative to the ground (Vg) can be calculated as:
Vg = Va + Vw
Substituting the given values:
Vg = 50 m/s (north) + (-5 m/s) (south)
Adding the velocities:
Vg = 50 m/s - 5 m/s
Simplifying,
Vg = 45 m/s
Therefore, the speed of the airplane relative to the ground at the time of landing is 45 m/s.