Q. 47 A bowling ball dropped from a he... [FREE SOLUTION]

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Chapter 2: Q. 47 (page 166)

A bowling ball dropped from a height of $400$ feet will be $s (t) = 400 - 16 t^{2}$ feet from the ground after $t$ seconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:
After $t = 2$ seconds, with $h = 0.1, h = 0.01 h = - 0.1 a n d h = - 0.01$

Short Answer

Expert verified

Ans: When $h = 0.1$ instantaneous velocity is: $- 65.4$

When $h = 0.01$ instantaneous velocity is: $- 65$

When $h = - 0.1$ instantaneous velocity is: $- 62.4$

When $h = - 0.01$ instantaneous velocity is: $- 64$

Step by step solution

Step 1. Given information.

given,

A ball is dropped from a height of $400$ feet and its distance from the ground after $t$ seconds is, $s (t) = 400 鈭� 16 t^{2}$
The objective is to estimate the instantaneous velocities for,

$t = 2 s, h = 0.1, h = 0.01, h = - 0.1 a n d h = - 0.01$

Step 2. To find the instantaneous velocity for h=0.1 follows the steps:

$f (t) = f (2) = 400 - 16 {(2)}^{2} = 336$

And

$f (t + h) = f (2.1) = 329.44$

Therefore the instantaneous velocity is:

$\begin{aligned} \frac{f (t + h) 鈭� f (t)}{h} = \frac{329.44 鈭� 336}{0.1} \\ = \frac{鈭� 6.54}{0.1} \\ = 鈭� 65.4 \end{aligned}$

Step 3. To find the instantaneous velocity for h=0.01 follows the steps:

$f (t) = f (2) = 336$

And

role="math" $f (t + h) = f (2.01) = 335.35$

Therefore the instantaneous velocity is:

$\begin{aligned} \frac{f (t + h) 鈭� f (t)}{h} = \frac{335.35 鈭� 336}{0.01} \\ = \frac{鈭� 0.65}{0.01} \\ = 鈭� 65 \end{aligned}$

Step 4. To find the instantaneous velocity for h=-0.1 follows the steps:

$f (t) = f (2) = 336$

And

$f (t + h) = f (1.9) = 342.24$

Therefore the instantaneous velocity is:

$\begin{aligned} \frac{f (t + h) 鈭� f (t)}{h} = \frac{342.24 鈭� 336}{鈭� 0.1} \\ = \frac{6.24}{鈭� 0.1} \\ = 鈭� 62.4 \end{aligned}$

f (t + h) = f (1.9) = 324.24

Step 5. To find the instantaneous velocity for h=-0.01 follows the steps:

$f (t) = f (2) = 336$

And, $f (t + h) = f (1.99) = 336.64$

Therefore the instantaneous velocity is:

$\begin{aligned} \frac{f (t + h) 鈭� f (t)}{h} = \frac{336.64 鈭� 336}{鈭� 0.2} \\ = \frac{0.64}{鈭� 0.01} \\ = 鈭� 64 \end{aligned}$

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91影视

A bowling ball dropped from a height of $400$ feet will be $s (t) = 400 - 16 t^{2}$ feet from the ground after $t$ seconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:
After $t = 2$ seconds, with $h = 0.1, h = 0.01 h = - 0.1 a n d h = - 0.01$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. To find the instantaneous velocity for h=0.1 follows the steps:

Step 3. To find the instantaneous velocity for h=0.01 follows the steps:

Step 4. To find the instantaneous velocity for h=-0.1 follows the steps:

Step 5. To find the instantaneous velocity for h=-0.01 follows the steps:

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91影视

A bowling ball dropped from a height of 400feet will be s(t)=400-16t2feet from the ground after tseconds. Use a sequence of average velocities to estimate the instantaneous velocities described below: After t=2 seconds, with h=0.1,h=0.01h=-0.1andh=-0.01

Short Answer

Step by step solution

Step 1. Given information.

Step 2. To find the instantaneous velocity for h=0.1 follows the steps:

Step 3. To find the instantaneous velocity for h=0.01 follows the steps:

Step 4. To find the instantaneous velocity for h=-0.1 follows the steps:

Step 5. To find the instantaneous velocity for h=-0.01 follows the steps:

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Logic and Functions

Theoretical and Mathematical Physics

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

A bowling ball dropped from a height of $400$ feet will be $s (t) = 400 - 16 t^{2}$ feet from the ground after $t$ seconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:
After $t = 2$ seconds, with $h = 0.1, h = 0.01 h = - 0.1 a n d h = - 0.01$