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

Question

Want to see the full answer?

Answer 1

Question

Chapter 4.7, Problem 75E

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

Students have asked these similar questions

1- √ √ √³ e³/√xdy dx 1 cy² 2- √ √² 3 y³ exy dx dy So 3- √ √sinx y dy dx 4- Jo √² Sy² dx dy

A building that is 205 feet tall casts a shadow of various lengths æ as the day goes by. An angle of elevation is formed by lines from the top and bottom of the building to the tip of the shadow, as de seen in the following figure. Find the rate of change of the angle of elevation when x 278 feet. dx Round to 3 decimal places. Γ X radians per foot

Use the information in the following table to find h' (a) at the given value for a. x|f(x) g(x) f'(x) g(x) 0 0 0 4 3 1 4 4 3 0 2 7 1 2 7 3 3 1 2 9 4 0 4 5 7 h(x) = f(g(x)); a = 0 h' (0) =

Answer 2

Question

Chapter 4.7, Problem 75E

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 4.7, Problem 75E

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 4.7, Problem 75E

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 4.7, Problem 75E

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 4.7, Problem 75E

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 4.7, Problem 75E

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

Want to see the full answer?

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