A basketball player stands d feet from the basket let h and α ball θ υ 2 = 1 6 d c o s 2 q ( t a n q - t a n a ) a) α < θ < π 2 why does υ approach infinity at the endpoints of this interval

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Answer 1

Question

Chapter 4.6, Problem 73E

To determine

A basketball player stands $d$ feet from the basket let $h$ and $α$ ball $θ$ $υ^{2} = \frac{16 d}{c o s^{2} q (t a n q - t a n a)}$

a)

$α < θ < \frac{π}{2}$ why does $υ$ approach infinity at the endpoints of this interval

To determine

b)

$α \frac{π}{6}$ And plot $υ^{2}$ as a fraction of $θ$ for $\frac{π}{6} < θ < \frac{π}{2}$ verify that the minimum occurs at $θ = \frac{π}{3}$

To determine

c)

Set $F (θ) = \cos^{2} θ (\tan θ - \tan α)$ why $υ$ is minimized for $θ$ such that $F (θ)$ is maximized

To determine

d)

Verify that $F' (θ) = \cos (α - 2 θ) \sec α$ additional formula used maximum value $F$

To determine

e)

For a give $α$ the optimal angle for shooting the basket $θ_{o}$ cause it minimizes $υ^{2}$

To determine

f)

Show with graph that for fixed $d$ $υ^{2}_{o p t}$ is an increasing function of $h$

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Answer 2

Question

Chapter 4.6, Problem 73E

To determine

A basketball player stands $d$ feet from the basket let $h$ and $α$ ball $θ$ $υ^{2} = \frac{16 d}{c o s^{2} q (t a n q - t a n a)}$

a)

$α < θ < \frac{π}{2}$ why does $υ$ approach infinity at the endpoints of this interval

To determine

b)

$α \frac{π}{6}$ And plot $υ^{2}$ as a fraction of $θ$ for $\frac{π}{6} < θ < \frac{π}{2}$ verify that the minimum occurs at $θ = \frac{π}{3}$

To determine

c)

Set $F (θ) = \cos^{2} θ (\tan θ - \tan α)$ why $υ$ is minimized for $θ$ such that $F (θ)$ is maximized

To determine

d)

Verify that $F' (θ) = \cos (α - 2 θ) \sec α$ additional formula used maximum value $F$

To determine

e)

For a give $α$ the optimal angle for shooting the basket $θ_{o}$ cause it minimizes $υ^{2}$

To determine

f)

Show with graph that for fixed $d$ $υ^{2}_{o p t}$ is an increasing function of $h$

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 4.6, Problem 73E

To determine

A basketball player stands $d$ feet from the basket let $h$ and $α$ ball $θ$ $υ^{2} = \frac{16 d}{c o s^{2} q (t a n q - t a n a)}$

a)

$α < θ < \frac{π}{2}$ why does $υ$ approach infinity at the endpoints of this interval

To determine

b)

$α \frac{π}{6}$ And plot $υ^{2}$ as a fraction of $θ$ for $\frac{π}{6} < θ < \frac{π}{2}$ verify that the minimum occurs at $θ = \frac{π}{3}$

To determine

c)

Set $F (θ) = \cos^{2} θ (\tan θ - \tan α)$ why $υ$ is minimized for $θ$ such that $F (θ)$ is maximized

To determine

d)

Verify that $F' (θ) = \cos (α - 2 θ) \sec α$ additional formula used maximum value $F$

To determine

e)

For a give $α$ the optimal angle for shooting the basket $θ_{o}$ cause it minimizes $υ^{2}$

To determine

f)

Show with graph that for fixed $d$ $υ^{2}_{o p t}$ is an increasing function of $h$

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 4.6, Problem 73E

To determine

A basketball player stands $d$ feet from the basket let $h$ and $α$ ball $θ$ $υ^{2} = \frac{16 d}{c o s^{2} q (t a n q - t a n a)}$

a)

$α < θ < \frac{π}{2}$ why does $υ$ approach infinity at the endpoints of this interval

To determine

b)

$α \frac{π}{6}$ And plot $υ^{2}$ as a fraction of $θ$ for $\frac{π}{6} < θ < \frac{π}{2}$ verify that the minimum occurs at $θ = \frac{π}{3}$

To determine

c)

Set $F (θ) = \cos^{2} θ (\tan θ - \tan α)$ why $υ$ is minimized for $θ$ such that $F (θ)$ is maximized

To determine

d)

Verify that $F' (θ) = \cos (α - 2 θ) \sec α$ additional formula used maximum value $F$

To determine

e)

For a give $α$ the optimal angle for shooting the basket $θ_{o}$ cause it minimizes $υ^{2}$

To determine

f)

Show with graph that for fixed $d$ $υ^{2}_{o p t}$ is an increasing function of $h$

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 4.6, Problem 73E

To determine

A basketball player stands $d$ feet from the basket let $h$ and $α$ ball $θ$ $υ^{2} = \frac{16 d}{c o s^{2} q (t a n q - t a n a)}$

a)

$α < θ < \frac{π}{2}$ why does $υ$ approach infinity at the endpoints of this interval

To determine

b)

$α \frac{π}{6}$ And plot $υ^{2}$ as a fraction of $θ$ for $\frac{π}{6} < θ < \frac{π}{2}$ verify that the minimum occurs at $θ = \frac{π}{3}$

To determine

c)

Set $F (θ) = \cos^{2} θ (\tan θ - \tan α)$ why $υ$ is minimized for $θ$ such that $F (θ)$ is maximized

To determine

d)

Verify that $F' (θ) = \cos (α - 2 θ) \sec α$ additional formula used maximum value $F$

To determine

e)

For a give $α$ the optimal angle for shooting the basket $θ_{o}$ cause it minimizes $υ^{2}$

To determine

f)

Show with graph that for fixed $d$ $υ^{2}_{o p t}$ is an increasing function of $h$

Answer 6

Chapter 4.6, Problem 73E

To determine

A basketball player stands $d$ feet from the basket let $h$ and $α$ ball $θ$ $υ^{2} = \frac{16 d}{c o s^{2} q (t a n q - t a n a)}$

a)

$α < θ < \frac{π}{2}$ why does $υ$ approach infinity at the endpoints of this interval

Answer 7

Chapter 4.6, Problem 73E

To determine

A basketball player stands $d$ feet from the basket let $h$ and $α$ ball $θ$ $υ^{2} = \frac{16 d}{c o s^{2} q (t a n q - t a n a)}$

a)

$α < θ < \frac{π}{2}$ why does $υ$ approach infinity at the endpoints of this interval

Answer 8

To determine

b)

$α \frac{π}{6}$ And plot $υ^{2}$ as a fraction of $θ$ for $\frac{π}{6} < θ < \frac{π}{2}$ verify that the minimum occurs at $θ = \frac{π}{3}$

Answer 9

To determine

b)

$α \frac{π}{6}$ And plot $υ^{2}$ as a fraction of $θ$ for $\frac{π}{6} < θ < \frac{π}{2}$ verify that the minimum occurs at $θ = \frac{π}{3}$

Answer 10

To determine

c)

Set $F (θ) = \cos^{2} θ (\tan θ - \tan α)$ why $υ$ is minimized for $θ$ such that $F (θ)$ is maximized

Answer 11

To determine

c)

Set $F (θ) = \cos^{2} θ (\tan θ - \tan α)$ why $υ$ is minimized for $θ$ such that $F (θ)$ is maximized

Answer 12

To determine

d)

Verify that $F' (θ) = \cos (α - 2 θ) \sec α$ additional formula used maximum value $F$

Answer 13

To determine

d)

Verify that $F' (θ) = \cos (α - 2 θ) \sec α$ additional formula used maximum value $F$

Answer 14

To determine

e)

For a give $α$ the optimal angle for shooting the basket $θ_{o}$ cause it minimizes $υ^{2}$

Answer 15

To determine

e)

For a give $α$ the optimal angle for shooting the basket $θ_{o}$ cause it minimizes $υ^{2}$

Answer 16

To determine

f)

Show with graph that for fixed $d$ $υ^{2}_{o p t}$ is an increasing function of $h$

Answer 17

To determine

f)

Show with graph that for fixed $d$ $υ^{2}_{o p t}$ is an increasing function of $h$

Answer 18

Expert Solution & Answer

Answer 19

Expert Solution & Answer

Answer 20

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Check out a sample textbook solution

See solution

Answer 21

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

A basketball player stands d feet from the basket let h and α ball θ υ 2 = 1 6 d c o s 2 q ( t a n q - t a n a ) a) α &lt; θ &lt; π 2 why does υ approach infinity at the endpoints of this interval