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(Point of no return) As a plane is accelerating to prepare for takeoff, there is a certain point when it can no longer abort the takeoff due to there not being enough runway remaining for it to come to a stop. We will call this the point of no return. In this problem, we will investigate this point, both in space and in time! (a) Suppose during takeoff, the plane achieves a constant acceleration of 5 m/s2. Find a formula for the function v(t) := velocity of the plane at time t (We assume that the pilot begins the takeoff at time t = 0 at the beginning of the runway). (b) Find a formula for the function d(t) := the distance traveled at time t (c) Suppose that in the event that takeoff needs to be cancelled, the plane can decelerate at a rate of at most - 8 m/s2. Find a formula for the function r(t) := The amount of additional runway required in case the pilot needs to abort takeoff at time t (d) Suppose the runway is 500m long. How long will it take for the plane to reach the point of no return? First give the exact answer. Then, using a calculator, write the answer to 2 decimal places. (e) How far along the runway is the point of no return? First give the exact answer, then using a calculator, write the answer to 2 decimal places. (f) The minimum takeoff speed is the minimum speed required for the plane to become airborne. Suppose the minimum takeoff speed for our plane is 65 m/s. Will the plane be able to take off on our runway? (g) Will there be an interval in time when the plane is past the point of no return but still not airborne? How long is this interval? First give the exact answer. Then, using a calculator, write the answer to 2 decimal places. (h) Suppose you wanted to design a runway where it is safe for our plane to abort takeoff all the way up until the actual point of the plane becoming airborne. What is the minimum length for such a runway? First give the exact answer. Then, using a calculator, write the answer to 2 decimal places.

(Point of no return) As a plane is accelerating to prepare for takeoff, there is a certain point when it can no longer abort the takeoff due to there not being enough runway remaining for it to come to a stop. We will call this the point of no return. In this problem, we will investigate this point, both in space and in time! (a) Suppose during takeoff, the plane achieves a constant acceleration of 5 m/s2. Find a formula for the function v(t) := velocity of the plane at time t (We assume that the pilot begins the takeoff at time t = 0 at the beginning of the runway). (b) Find a formula for the function d(t) := the distance traveled at time t (c) Suppose that in the event that takeoff needs to be cancelled, the plane can decelerate at a rate of at most - 8 m/s2. Find a formula for the function r(t) := The amount of additional runway required in case the pilot needs to abort takeoff at time t (d) Suppose the runway is 500m long. How long will it take for the plane to reach the point of no return? First give the exact answer. Then, using a calculator, write the answer to 2 decimal places. (e) How far along the runway is the point of no return? First give the exact answer, then using a calculator, write the answer to 2 decimal places. (f) The minimum takeoff speed is the minimum speed required for the plane to become airborne. Suppose the minimum takeoff speed for our plane is 65 m/s. Will the plane be able to take off on our runway? (g) Will there be an interval in time when the plane is past the point of no return but still not airborne? How long is this interval? First give the exact answer. Then, using a calculator, write the answer to 2 decimal places. (h) Suppose you wanted to design a runway where it is safe for our plane to abort takeoff all the way up until the actual point of the plane becoming airborne. What is the minimum length for such a runway? First give the exact answer. Then, using a calculator, write the answer to 2 decimal places.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(Point of no return) As a plane is accelerating to prepare for takeoff, there is a certain point when it can no longer abort the takeoff due to there not being enough runway remaining for it to come to a stop. We will call this the point of no return. In this problem, we will investigate this point, both in space and in time! (a) Suppose during takeoff, the plane achieves a constant acceleration of 5 m/s2. Find a formula for the function v(t) := velocity of the plane at time t (We assume that the pilot begins the takeoff at time t = 0 at the beginning of the runway). (b) Find a formula for the function d(t) := the distance traveled at time t (c) Suppose that in the event that takeoff needs to be cancelled, the plane can decelerate at a rate of at most - 8 m/s2. Find a formula for the function r(t) := The amount of additional runway required in case the pilot needs to abort takeoff at time t (d) Suppose the runway is 500m long. How long will it take for the plane to reach the point of no return? First give the exact answer. Then, using a calculator, write the answer to 2 decimal places. (e) How far along the runway is the point of no return? First give the exact answer, then using a calculator, write the answer to 2 decimal places. (f) The minimum takeoff speed is the minimum speed required for the plane to become airborne. Suppose the minimum takeoff speed for our plane is 65 m/s. Will the plane be able to take off on our runway? (g) Will there be an interval in time when the plane is past the point of no return but still not airborne? How long is this interval? First give the exact answer. Then, using a calculator, write the answer to 2 decimal places. (h) Suppose you wanted to design a runway where it is safe for our plane to abort takeoff all the way up until the actual point of the plane becoming airborne. What is the minimum length for such a runway? First give the exact answer. Then, using a calculator, write the answer to 2 decimal places.
Transcribed Image Text:(Point of no return) As a plane is accelerating to prepare for takeoff, there is a certain point when it can no longer abort the takeoff due to there not being enough runway remaining for it to come to a stop. We will call this the point of no return. In this problem, we will investigate this point, both in space and in time! (a) Suppose during takeoff, the plane achieves a constant acceleration of 5 m/s2. Find a formula for the function v(t) := velocity of the plane at time t (We assume that the pilot begins the takeoff at time t = 0 at the beginning of the runway). (b) Find a formula for the function d(t) := the distance traveled at time t (c) Suppose that in the event that takeoff needs to be cancelled, the plane can decelerate at a rate of at most - 8 m/s2. Find a formula for the function r(t) := The amount of additional runway required in case the pilot needs to abort takeoff at time t (d) Suppose the runway is 500m long. How long will it take for the plane to reach the point of no return? First give the exact answer. Then, using a calculator, write the answer to 2 decimal places. (e) How far along the runway is the point of no return? First give the exact answer, then using a calculator, write the answer to 2 decimal places. (f) The minimum takeoff speed is the minimum speed required for the plane to become airborne. Suppose the minimum takeoff speed for our plane is 65 m/s. Will the plane be able to take off on our runway? (g) Will there be an interval in time when the plane is past the point of no return but still not airborne? How long is this interval? First give the exact answer. Then, using a calculator, write the answer to 2 decimal places. (h) Suppose you wanted to design a runway where it is safe for our plane to abort takeoff all the way up until the actual point of the plane becoming airborne. What is the minimum length for such a runway? First give the exact answer. Then, using a calculator, write the answer to 2 decimal places.
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