A jetliner, traveling northward, is landing with a speed of 66.5 m/s. Once the jet touches down, it has 766 m of runway in which to reduce its speed to 13.1 m/s. Compute the average acceleration (magnitude and direction) of the plane during landing (take the direction of the plane's motion as positive).
To compute the average acceleration of the plane during landing, we can use the formula:
Acceleration = (Final velocity - Initial velocity) / Time
In this case, the initial velocity (u) is 66.5 m/s, the final velocity (v) is 13.1 m/s, and we need to find the time it takes for the plane to reduce its speed.
First, we need to find the time by using the formula for average velocity:
Average velocity = (Initial velocity + Final velocity) / 2
Since the jetliner is traveling in a straight line and the average velocity is given by the displacement divided by time, we can write:
Average velocity = Displacement / Time
Rearranging the equation to find time:
Time = Displacement / Average velocity
Given that the displacement is 766 m, and the Average velocity is (66.5 m/s + 13.1 m/s) / 2 = 39.8 m/s, we can calculate:
Time = 766 m / 39.8 m/s ≈ 19.25 s
Now, we can substitute the values into the acceleration formula:
Acceleration = (Final velocity - Initial velocity) / Time
Acceleration = (13.1 m/s - 66.5 m/s) / 19.25 s
Simplifying:
Acceleration = (-53.4 m/s) / 19.25 s
Acceleration ≈ -2.77 m/s²
Therefore, the magnitude of the average acceleration of the plane during landing is 2.77 m/s², and the direction is negative (southward).