The required take-off speed of a commercial airplane is 120 knots. if  this commercial aeroplane take 30-seconds to eovers the airport runaway path, calculate the

a) Accerleration required during take off

b) Runaway length of airport

Solution:

a) To calculate the acceleration required during takeoff, we need to use the following formula:

acceleration = `(takeoff speed)^2 / (2 * runway length)`

We know that the takeoff speed is 120 knots. To convert knots to meters per second, we multiply by 0.5144:

120 knots * 0.5144 = 61.7 meters per second

We also know that the time it takes to cover the runway is 30 seconds. Therefore, the runway length can be calculated as:

runway length = takeoff speed * time

runway length = 120 knots * 0.5144 m/s per knot * 30 seconds

runway length = 1860 meters

Now we can plug these values into the acceleration formula:

acceleration = `(61.7 m/s)^2 / (2 * 1860 m)`

acceleration = 1.028 m/s^2

Therefore, the required acceleration during takeoff is 1.028 m/s^2.

b) To calculate the runaway length of the airport, we can use the formula:

runway length = takeoff speed * time

We already know that the takeoff speed is 120 knots and the time to cover the runway is 30 seconds. Therefore:

runway length = 120 knots * 0.5144 m/s per knot * 30 seconds

runway length = 1860 meters

Therefore, the runaway length of the airport is 1860 meters.

OR

To solve the given problem, we can use the equations of motion to calculate the acceleration required during takeoff and the runaway length of the airport.

a) To find the acceleration required during takeoff, we can use the equation:

v = u + at

where:

v = final velocity (in knots) = 120 knots (given)

u = initial velocity (in knots) = 0 knots (as the plane is at rest before takeoff)

t = time taken to reach final velocity = 30 seconds (given)

Rearranging the equation, we get:

a = (v - u) / t

a = (120 - 0) / 30

a = 4 knots/second

Therefore, the acceleration required during takeoff is 4 knots/second.

b) To find the runaway length of the airport, we can use the equation:

s = ut + 1/2 at^2

where:

s = runaway length (in nautical miles)

u = initial velocity (in knots) = 0 knots (as the plane is at rest before takeoff)

t = time taken to reach final velocity = 30 seconds (given)

a = acceleration (in knots/second) = 4 knots/second (calculated above)

Converting the units to nautical miles and seconds, we get:

s = (0.5) * (4/6076) * (30^2)

s = 0.382 nautical miles

Therefore, the runaway length of the airport is 0.382 nautical miles.

Note: It is important to double-check the units and use consistent units throughout the calculations.