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

BuyFind*launch*

4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 4.8, Problem 43E

(a)

To determine

**To find**: The distance of stone above the ground level.

Expert Solution

The distance of stone above ground level at time *t* is

**Given data:**

The distance between upper observation deck and ground is 450 m.

**Formula used:**

Write the expression for acceleration function

Here,

Write the expression for velocity function

Here,

Antiderivative of

**Calculation:**

At first observation, velocity is zero and position is at 450 m at

The motion of stone is close to ground, so the motion is considered as gravitational constant

Write the expression for acceleration function

Substitute

Antiderivate the expression with respect to *t*,

Here,

*C* is arbitrary constant.

Substitute 0 for *t* in equations (3),

Substitute 0 for

Substitute 0 for *C* in equation (3),

Substitute

Antiderivate the expression with respect to *t*.

Here,

*D* is arbitrary constant.

Substitute 0 for *t* in equation (6),

Substitute 450 for

Substitute 450 for *D* in equation (6),

Thus, the distance of stone above ground level at time *t* is

(b)

To determine

**To find**: The time that stone takes to reach ground.

Expert Solution

The time that stone takes to reach ground is 9.58 seconds.

**Given data:**

The distance between upper observation deck and ground is 450 m.

**Calculation:**

When the stone reaches the ground, the positional function reaches zero. Hence,

Substitute

Take square root on both sides.

Thus, the time that stone takes to reach ground is 9.58 seconds.

(c)

To determine

**To find**: The velocity that stone strikes the ground.

Expert Solution

The velocity that stone strikes the ground is

**Given data:**

The distance between upper observation deck and ground is 450 m.

**Calculation:**

Substitute 9.58 seconds for *t* in equation (5),

Thus, the velocity that stone strikes the ground is

(d)

To determine

**To find**: The time that stone takes to reach ground.

Expert Solution

The time that stone takes to reach ground, when it is thrown downward with speed of

**Given data:**

The speed is

**Formula used:**

Write the expression to find the roots of

Here,

*a*, *b*, and *c* are constants.

**Calculation:**

The stone is thrown downwards with a speed of

Substitute –5 for

Substitute –5 for *C* in equation (3),

Substitute

Antiderivate the expression with respect to *t*,

Here,

*D* is arbitrary constant.

Substitute 0 for *t* in equation (9),

Substitute 450 for

Substitute 450 for *D* in equation (9),

Substitute

Compare the expressions

Substitute 4.9 for *a*, 5 for *b*, and –450 for *c* in equation (8),

Hence, the two possible values of *t* are,

The time cannot be a negative, so the value of *t* is 9.09 seconds.

Thus, the time that stone takes to reach ground, when it is thrown downward with speed of