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CalculusCalculus10th Edition

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Chapter 12.4, Problem 63E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem
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Projectile Motion A projectile is launched with an initial velocity of 120 feet per second at a height of 5 feet and at an angle of 30 ∘ with the horizontal.

(a) Determine the vector-valued function for the path of the projectile.

(b) Use a graphing utility to graph the path and approximate the maximum height and range of the projectile.

(c) Find v ( t ) , ‖ v ( t ) ‖ , and a(t).

(d) Use a graphing utility to complete the table.

t

0.5

1.0

1.5

2.0

2.5

3.0

Speed

(e) Use a graphing utility to graph the scalar functions a T and a N . How is the speed of the projectile changing when a T and a N have opposite signs?

(a)

To determine

To calculate: The vector-valued function for the path of the projectile.

Explanation

Given:

θ=30∘,v0=120ft/sec,h=5ft,g=32ft/s2

Formula used:

r(t)=(v0cosθ)ti+(h+(v0sinθ)t−12gt2)j

Calculation:

The path of the projectile of a vector-valued function is given by,

r(t)=(v0cosθ)t

(b)

To determine

To graph: The path of the projectile and approximate maximum height and range of projectile of given function.

(c)

To determine

To calculate: The values of v(t),‖v(t)‖,a(t).

(d)

To determine

To calculate: The values to complete the table.

(e)

To determine

To graph: The scalar functions aT and aN

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Sect-12.1 P-1ESect-12.1 P-2ESect-12.1 P-3ESect-12.1 P-4ESect-12.1 P-5ESect-12.1 P-6ESect-12.1 P-7ESect-12.1 P-8ESect-12.1 P-9ESect-12.1 P-10E
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