Answer: Runway length: 81.6 m
Take-off time: 15.4 seconds
Explanation: The runway length needed for a plane to accelerate from rest to a take-off speed of 50 m/s at a comfortable acceleration of 0.3g or 3.27 m/s² can be calculated using the following formula:
Runway length = (final velocity)² / (2 * acceleration)
Plugging in the values, we get:
Runway length = (50 m/s)² / (2 * 3.27 m/s²) = 81.6 m
Therefore, the plane needs a runway of at least 81.6 meters to accelerate to take-off speed.
The time it takes for the plane to reach take-off speed can be calculated using the following formula:
Time = (final velocity) / acceleration
Plugging in the values, we get:
Time = 50 m/s / 3.27 m/s² = 15.4 seconds
Therefore, it takes the plane 15.4 seconds to reach take-off speed.