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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.5, Problem 112E

To determine

The speed of the ball at which it should be thrown upward to reach a maximum height of

Expert Solution

The speed of the ball at which it should be thrown upward to reach a maximum height of

**Given:**

An object thrown or fired straight upward at an initial speed of *h* feet after *t* seconds, where *h* and *t* are related by the formula

**Result used:**

*Discriminant of a quadratic equation:*

The quantity

1. If

2. If

3. If

**Calculation:**

Substitute

Compare this equation with the general form

Here

Note that, the ball will reach the highest point only once and the quadratic equation has only one solution when the discriminant is zero.

Therefore, let the discriminant be zero.

On further simplifications, the following is obtained.

Since the speed should be always positive, the value of

Thus, the speed of the ball at which it should be thrown upward to reach a maximum height of