A jetliner, traveling northward, is landing with a speed of 67 m/s. Once the jet touches down, it has 765 m of runway in which to reduce its speed to 5.1 m/s. Compute the average acceleration (magnitude and direction) of the plane during landing (take the positive direction to be northward).
(Vf)^2 = Vo^2 + 2a*d,
a = (Vf^2-Vo^2)/2d,
a=((5.1)^2-(67)^2) / 1530 = -2.92m/s^2.
Negative acceleration means that the plane is slowing down.
To compute the average acceleration of the plane during landing, we can use the equation:
average acceleration = (final velocity - initial velocity) / time
In this case, we're given the initial velocity (67 m/s) and the final velocity (5.1 m/s). However, we need to find the time it takes for the plane to decelerate from 67 m/s to 5.1 m/s.
To find the time, we can use the equation of motion:
final velocity² = initial velocity² + 2 * acceleration * distance
Rearranging the equation to solve for acceleration, we get:
acceleration = (final velocity² - initial velocity²) / (2 * distance)
Plugging in the values, we have:
acceleration = (5.1² - 67²) / (2 * 765)
Simplifying the equation, we get:
acceleration = (-4302.9) / 1530
Therefore, the average acceleration of the plane during landing is approximately -2.81 m/s² (with the negative sign indicating a deceleration) in the northward direction.