a plane travelling north has a landing speed of 75.6m/s. after touch down it has 787m long runway to reduce its speed to 15.9m/s. calculate average acceleration of the plane during landing taking the direction of the plane travels as positive
if v is + and it slows down a is - , (deacceleration)
change in velocity = - 75.6
time to stop = distance /mean velocity = 787 / mean velocity
because velocity vs time is linear mean velocity = 75.6/2 = 37.8
so t = 787 /37.8 = 20.8 m/s
a = change in velocity / time = -75.6 / 20.8 m/s^2
so my answer is 13.21?
-75.6 divided by 20.8 is not 13.21
To calculate the average acceleration of the plane during landing, we'll use the formula:
average acceleration = (final velocity - initial velocity) / time
First, let's convert the given speeds from m/s to km/h for consistency:
Initial velocity (u) = 75.6 m/s = (75.6 * 3600) km/h = 271.44 km/h
Final velocity (v) = 15.9 m/s = (15.9 * 3600) km/h = 57.24 km/h
Next, we need to find the time it takes for the plane to reduce its speed. We can use the formula:
distance = (initial velocity + final velocity) / 2 * time
Rearranging the formula for time, we have:
time = distance / ( (initial velocity + final velocity) / 2 )
Plugging in the given values:
distance = 787 m
initial velocity = 75.6 m/s
final velocity = 15.9 m/s
time = 787 / ( (75.6 + 15.9) / 2 ) = 787 / (91.5 / 2 ) = 787 / 45.75 = 17.19 s
Now we can calculate the average acceleration:
average acceleration = (final velocity - initial velocity) / time
= (15.9 - 75.6) / 17.19
= -59.7 / 17.19
= -3.47 m/s²
Since we took the direction of the plane's travel as positive, the negative sign indicates that the acceleration is in the opposite direction (i.e., slowing down).
Therefore, the average acceleration of the plane during landing is approximately -3.47 m/s².