A jetliner, traveling northward, is landing with a speed of 72 m/s. Once the jet touches down, it has 730 m of runway in which to reduce its speed to 5.9 m/s. Compute the average acceleration (magnitude and direction) of the plane during landing (take the positive direction to be northward).
The acceleration (a) must be southward to slow the plane down. An equation you can use is:
2 a X = [V2^2 - V1^2]
where V2 = 5.9 m/s and V1 = 72 m/s
Solve for a. It will be negative (meaning the opposite or northward)
t=0
To compute the average acceleration of the plane during landing, we can use the formula:
average acceleration = change in velocity / time taken
First, let's calculate the change in velocity. The initial velocity of the plane is 72 m/s (northward) and the final velocity is 5.9 m/s (northward).
change in velocity = final velocity - initial velocity
change in velocity = 5.9 m/s - 72 m/s
change in velocity = -66.1 m/s
The negative sign indicates that the direction of the change in velocity is opposite to the initial velocity.
Now, let's calculate the time taken to achieve this change in velocity. We can use the formula:
distance = (initial velocity + final velocity) / 2 * time
In this case, the distance is 730 m, the initial velocity is 72 m/s, the final velocity is 5.9 m/s, and we need to solve for time.
730 = (72 + 5.9) / 2 * time
1460 = 77.9 * time
time = 1460 / 77.9
time ≈ 18.76 seconds
Now that we have both the change in velocity and the time taken, we can calculate the average acceleration.
average acceleration = change in velocity / time taken
average acceleration = -66.1 m/s / 18.76 s
Calculating this gives us:
average acceleration ≈ -3.52 m/s²
Therefore, the magnitude of the average acceleration of the plane during landing is approximately 3.52 m/s². The negative sign indicates that the acceleration is in the opposite direction of the initial velocity, which is southward.