Explanation 1) Concept: Solving an expression is to find the value of unknown in the expression, which on substitution must satisfy the expression. 2) Calculation: Given, Length of the runway = 800 ft . Equation relating the length of the runway ‘D’ in feet and the landing speed ‘ s ’ in second is, D = 0.1 s 2 − 3 s + 22 Here ‘D’ cannot exceed 800 feet as the plane will run away from the runway and also it cannot be less than 800 ft, as the plane may stall when the speed is less. Hence, D = 800 800 = 0.1 s 2 − 3 s + 22 Add − 800 on both sides, 800 − 800 = 0.1 s 2 − 3 s + 22 − 800 0.1 s 2 − 3 s − 778 = 0 Multiply each term by 10 on both sides, ( 0.1 s 2 ) 10 − 3 s ⋅ 10 − 778 ⋅ 10 = 0 Combining the like terms, [ ( 0.1 ) ⋅ 10 ] s 2 − ( 3 ⋅ 10 ) s − ( 778 ⋅ 10 ) = 0 1 ⋅ s 2 − 30 ⋅ s − 7780 = 0 s 2 − 30 s − 7780 = 0 s 2 − 30 s − 7780 = 0 By the quadratic formula, s = − b ± b 2 − 4 a c 2 a ; Here, a = 1 , b = − 30 and c = − 7780

12th Edition

ISBN: 9780135963630

Author: Lial

Publisher: PEARSON CO

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Question

Chapter 1.CR, Problem 58CR

To determine

To find:

The appropriate landing speed of a small airplane, such that the initial landing speed ‘s’ in feet per second and the length of the runway ‘D’ in feet are related by D=0.1s2−3s+22, here the runway is 800 ft long and the plane should not be too fast as it may run out of the runway and it too slow, the plane may stall.

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Chapter 1.CR, Problem 57CR

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