(a) To determine The vector equation for path of baseball. Explanation From Example 5, the initial velocity is υ 0 = 152 ft/sec , the launch angle is α = 20 ° . Also a component of − 17.6 i ft/sec is added to the initial velocity and assume a drag coefficient k = 0.08 . Then using the linear drag from Exercise 41, obtain the distance downrange as follows. x = υ 0 cos α − 17.6 k ( 1 − e − k t ) = ( 152 cos 20 ° − 17.6 ) 0.08 ( 1 − e − 0.08 t ) Obtain the height of the projectile as shown below. y = 3 + υ 0 k ( 1 − e − k t ) ( sin α ) + g k 2 ( 1 − k t − e − k t ) = 3 + 152 0.08 ( 1 − e − 0.08 t ) ( sin 20 ° ) + 32 ( 0.08 ) 2 ( 1 − 0.08 t − e − 0.08 t ) Obtain the vector equation for path of the baseball as follows. r = x i + y j = { ( 152 cos 20 ° − 17 (b) To determine The maximum height reached by baseball and the time it reaches the maximum height. (c) To determine The flight time and range of the baseball. (d) To determine The time when the baseball is at 35 ft height and the distance downrange at that height. (e) To determine To explain: Whether the batter hit a home run or not.

Thomas' Calculus: Early Transcendentals (14th Edition)

14th Edition

ISBN: 9780134439020

Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher: PEARSON

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Question

Chapter 13.2, Problem 47E

(a)

To determine

The vector equation for path of baseball.

(b)

To determine

The maximum height reached by baseball and the time it reaches the maximum height.

(c)

To determine

The flight time and range of the baseball.

(d)

To determine

The time when the baseball is at 35 ft height and the distance downrange at that height.

(e)

To determine

To explain: Whether the batter hit a home run or not.

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Chapter 13.2, Problem 46E

Chapter 13.2, Problem 48E

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Chapter 13 Solutions

Thomas' Calculus: Early Transcendentals (14th Edition)

Ch. 13.1 - In Exercises 1–4, find the given limits. 1. Ch. 13.1 - In Exercises 1–4, find the given limits. 2. Ch. 13.1 - In Exercises 1–4, find the given limits. 3. Ch. 13.1 - In Exercises 1–4, find the given limits. 4. Ch. 13.1 - Motion in the Plane In Exercises 5–8, r(t) is the...Ch. 13.1 - Motion in the Plane In Exercises 5–8, r(t) is the...Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

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