Question

You have been hired by a firm that is designing a runway for an airport. Your job is to confirm that the runway is long enough for an airplane to land, but not unnecessarily long. You are given the velocity data for the largest aircraft that will land at the airport. The velocity data will be used to calculate the distance required for the aircraft to safely land and come to a stop. Below is a set of data that represents the velocity (in feet per second) of the final 45 seconds of the landing. At t = 0, the plane is on its final descent.

t in seconds 0 5 10 15 20 25 30 35 40 45
v(t) in mph 187 152.18 122.2 96.41 74.21 55.1 38.64 24.49 12.3 1.81


t in seconds 9 10 19 20 29 30 39 40 44 45
v(t) in mph 127.84 122.2 78.38 74.21 41.74 38.64 14.6 12.3 3.79 1.81

Required:
Describe the purpose and problem statement of this report. How do you think you will use calculus to ensure that the runway is sufficient? How are the velocity data useful?

Answer 1

The purpose of this statement is to enable the firm design an appropriate Runway with the necessary distance that would accommodate different planes with various velocities that would be landing and taking off at the Airport without skidding off and this can be achieved by calculating the Average Velocity of the given data .

note : Velocity = displacement / time

and Displacement in this context represents the Distance of the Runway.

Calculus can be used in the calculation of instanteous acceleration at different time intervals given

Explanation:

The purpose of this statement is to enable the firm design an appropriate Runway with the necessary distance that would accommodate different planes with various velocities that would be landing and taking off at the Airport without skidding off and this can be achieved by calculating the Average Velocity of the given data .

note : Velocity = displacement / time

and Displacement in this context represents the Distance of the Runway.

Calculus can be used in the calculation of instanteous acceleration at different time intervals given

i.e. when : t = 5, t = 10 , t = 15 ............ t = 45

instanteous acceleration Δ =
`(d(V(t))/(dt)`

where V(t) is velocity at the different intervals