Start your trial now! First week only $4.99!*arrow_forward*

BuyFind*launch*

6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.5, Problem 111E

(a)

To determine

The time taken by the ball to reach a height of

Expert Solution

The ball reaches a 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

**Calculation:**

The height of the ball is given as

Therefore, substitute

Simplify further as follows.

On further simplifications, the following is obtained.

Thus, the ball reaches a height of

(b)

To determine

The time taken by the ball to reach a height of

Expert Solution

The ball

**Formula used:**

*Quadratic formula:*

The solution of a quadratic equation of the form

**Calculation:**

The height of the ball is given as

Therefore, substitute

Simplify further as follows.

Compare this equation with the general form

Here

Use the quadratic formula to obtain the roots of the given equation.

Since the square of any real number is nonnegative,

Thus, the ball

(c)

To determine

The greatest height reached by the ball.

Expert Solution

The greatest height reached by the ball is

**Result used:**

*Discriminant of a quadratic equation:*

The quantity

1. If

2. If

3. If

**Calculation:**

Given that the height of an object thrown straight upward at an initial speed of *h* feet after *t* seconds, where *h* and *t* are related by the formula

Since the ball is thrown straight upward at an initial speed of

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.

Simplify the above equation as follows.

Thus, the greatest height reached by the ball is

(d)

To determine

The time taken by the ball to reach the highest point.

Expert Solution

The ball reaches the highest point after

The greatest height reached by the ball is obtained as

Substitute

Compare this equation with the general form

Here

Use the quadratic formula to obtain the roots of the given equation.

Simplify the above equation as follows.

Thus, the ball reaches the highest point after

(e)

To determine

The time taken by the ball to hit the ground.

Expert Solution

The ball hits the ground after

The height of a ball is

Substitute

Simplify further as follows.

That is,

Thus, the ball hits the ground after