Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of 45 ° to the horizontal, with a muzzle velocity of 50 feet per second. The height h of the projectile above the water is modelled by, h ( x ) = − 32 x 2 50 2 + x + 200 Where x is the horizontal distance of the projectile from the face of the cliff. a. At what horizontal distance from the face of the cliff is the height of the projectile a maximum?

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Answer 1

Question

Chapter 4.4, Problem 11AE

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

a. At what horizontal distance from the face of the cliff is the height of the projectile a maximum?

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

b. Find the maximum height of the projectile.

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

c. At what horizontal distance from the face of the cliff will the projectile strike the water?

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

d. Using a graphing utility, graph the function $h$ , $0 \leq x \leq 200$ .

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

e. Use a graphing utility to verify the solutions found in parts b. and c.

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

f. When the height of the projectile is 100 feet above the water, how far is it from the cliff?

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In simplest terms, Sketch the graph of the parabola. Then, determine its equation. opens downward, vertex is (- 4, 7), passes through point (0, - 39)

Answer 2

Question

Chapter 4.4, Problem 11AE

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

a. At what horizontal distance from the face of the cliff is the height of the projectile a maximum?

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

b. Find the maximum height of the projectile.

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

c. At what horizontal distance from the face of the cliff will the projectile strike the water?

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

d. Using a graphing utility, graph the function $h$ , $0 \leq x \leq 200$ .

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

e. Use a graphing utility to verify the solutions found in parts b. and c.

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

f. When the height of the projectile is 100 feet above the water, how far is it from the cliff?

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 3

Question

Chapter 4.4, Problem 11AE

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

a. At what horizontal distance from the face of the cliff is the height of the projectile a maximum?

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

b. Find the maximum height of the projectile.

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

c. At what horizontal distance from the face of the cliff will the projectile strike the water?

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

d. Using a graphing utility, graph the function $h$ , $0 \leq x \leq 200$ .

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

e. Use a graphing utility to verify the solutions found in parts b. and c.

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

f. When the height of the projectile is 100 feet above the water, how far is it from the cliff?

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 4.4, Problem 11AE

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

a. At what horizontal distance from the face of the cliff is the height of the projectile a maximum?

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

b. Find the maximum height of the projectile.

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

c. At what horizontal distance from the face of the cliff will the projectile strike the water?

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

d. Using a graphing utility, graph the function $h$ , $0 \leq x \leq 200$ .

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

e. Use a graphing utility to verify the solutions found in parts b. and c.

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

f. When the height of the projectile is 100 feet above the water, how far is it from the cliff?

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 4.4, Problem 11AE

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

a. At what horizontal distance from the face of the cliff is the height of the projectile a maximum?

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

b. Find the maximum height of the projectile.

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

c. At what horizontal distance from the face of the cliff will the projectile strike the water?

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

d. Using a graphing utility, graph the function $h$ , $0 \leq x \leq 200$ .

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

e. Use a graphing utility to verify the solutions found in parts b. and c.

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

f. When the height of the projectile is 100 feet above the water, how far is it from the cliff?

Answer 6

Chapter 4.4, Problem 11AE

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

a. At what horizontal distance from the face of the cliff is the height of the projectile a maximum?

Answer 7

Chapter 4.4, Problem 11AE

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

a. At what horizontal distance from the face of the cliff is the height of the projectile a maximum?

Answer 8

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

b. Find the maximum height of the projectile.

Answer 9

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

b. Find the maximum height of the projectile.

Answer 10

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

c. At what horizontal distance from the face of the cliff will the projectile strike the water?

Answer 11

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

c. At what horizontal distance from the face of the cliff will the projectile strike the water?

Answer 12

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

d. Using a graphing utility, graph the function $h$ , $0 \leq x \leq 200$ .

Answer 13

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

d. Using a graphing utility, graph the function $h$ , $0 \leq x \leq 200$ .

Answer 14

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

e. Use a graphing utility to verify the solutions found in parts b. and c.

Answer 15

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

e. Use a graphing utility to verify the solutions found in parts b. and c.

Answer 16

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

f. When the height of the projectile is 100 feet above the water, how far is it from the cliff?

Answer 17

To determine

To find: Analysing the Motion of a Projectile. A projectile is fired from a cliff 200 feet above the water at an inclination of $45 °$ to the horizontal, with a muzzle velocity of 50 feet per second. The height $h$ of the projectile above the water is modelled by,

$h (x) = \frac{- 32 x^{2}}{50^{2}} + x + 200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

f. When the height of the projectile is 100 feet above the water, how far is it from the cliff?

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. 1AYP Ch. 4.1 - Prob. 2AYP Ch. 4.1 - Prob. 3AYP Ch. 4.1 - Prob. 4AYP Ch. 4.1 - Prob. 5AYP Ch. 4.1 - Prob. 6AYP Ch. 4.1 - Prob. 7CV Ch. 4.1 - Prob. 8CV Ch. 4.1 - Prob. 9CV Ch. 4.1 - Prob. 10CV

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Chapter 4 Solutions