O'Reilly logo

Introductory Mathematics for Engineering Applications by Nathan W. Klingbeil, Kuldip S. Rattan

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Quadratic Equations in Engineering

CHAPTER 2

In this chapter, the applications of quadratic equations in engineering are introduced. It is assumed that students are familiar with this topic from their high school algebra course. A quadratic equation is a second-order polynomial equation in one variable that occurs in many areas of engineering. For example, the height of a ball thrown in the air can be represented by a quadratic equation. In this chapter, the solution of quadratic equations will be obtained by three methods: factoring, the quadratic formula, and completing the square.

2.1 A PROJECTILE IN A VERTICAL PLANE

Suppose a ball thrown upward from the ground with an initial velocity of 96 ft/s reaches a height h(t) after time t s as shown in Fig. 2.1. The height is expressed by the quadratic equation h(t) = 96 t − 16 t2 ft. Find the time t in seconds when h(t) = 80 ft.

Figure 2.1 A ball thrown upward to a height of h(t).

Solution:

h(t) = 96 t − 16 t2 = 80

or

Equation (2.1) is a quadratic equation of the form ax2 + bx + c = 0 and will be solved using three different methods.

Method 1: Factoring Dividing equation (2.1) by 16 yields

Equation (2.2) can be factored as

(

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required