A jetliner, traveling northward, is landing with a speed of 65 m/s. Once the jet touches down, it has 785 m of runway in which to reduce its speed to 5.0 m/s. Compute the average acceleration (magnitude and direction) of the plane during landing (take the positive direction to be northward).
To compute the average acceleration of the plane during landing, we need to use the formula:
average acceleration = (final velocity - initial velocity) / time
Here, the final velocity is 5.0 m/s (when the jetliner has reduced its speed), and the initial velocity is 65 m/s (when the jetliner is traveling northward).
First, let's find the time it takes for the jetliner to reduce its speed. Since we're given the distance (785 m) and the initial and final velocities, we can use the formula:
distance = (initial velocity + final velocity) / 2 * time
Rearranging the equation, we can solve for time:
time = (distance * 2) / (initial velocity + final velocity)
time = (785 m * 2) / (65 m/s + 5.0 m/s)
time = 1570 m / 70 m/s
time = 22.43 s
Now that we have the time, we can calculate the average acceleration:
average acceleration = (final velocity - initial velocity) / time
average acceleration = (5.0 m/s - 65 m/s) / 22.43 s
average acceleration = (-60 m/s) / 22.43 s
average acceleration ≈ -2.678 m/s²
The magnitude of the average acceleration is approximately 2.68 m/s², and the direction is southward (opposite to the positive direction, which is northward).