A jetliner, traveling northward, is landing with a speed of 62 m/s. Once the jet touches down, it has 700 m of runway in which to reduce its speed to 5.6 m/s. Compute the average acceleration (magnitude and direction) of the plane during landing (take the positive direction to be northward).
To find the average acceleration of the plane during landing, we can use the equation:
average acceleration = (change in velocity) / (time taken)
First, we need to find the change in velocity. The initial velocity of the plane is 62 m/s, and the final velocity is 5.6 m/s.
change in velocity = final velocity - initial velocity
= 5.6 m/s - 62 m/s
= -56.4 m/s
Note: We have a negative value because the plane is slowing down, and we took the positive direction to be northward.
Next, we need to find the time taken. We can use the equation:
distance = (initial velocity + final velocity) / 2 * time taken
Rearranging the equation to solve for time taken, we get:
time taken = (2 * distance) / (initial velocity + final velocity)
Plugging in the values, we have:
time taken = (2 * 700 m) / (62 m/s + 5.6 m/s)
= (1400 m) / (67.6 m/s)
≈ 20.71 s
Now we can calculate the average acceleration:
average acceleration = (change in velocity) / (time taken)
= (-56.4 m/s) / (20.71 s)
≈ -2.73 m/s²
Therefore, the magnitude of the average acceleration of the plane during landing is approximately 2.73 m/s², and the direction is southward (opposite to the positive direction, which is northward).