(a) Explanation Given: The projectileis travelling horizontally at 20 m/s and its position is relative to the origin ( 0 , 0 ) . The trajectory of the path followed by packet is x = ( 20 cos θ ) t , y = − 4.9 t 2 + ( 20 sin θ ) ; t ≥ 0 . Calculation: Substitute θ = π 6 in x = ( 20 cos θ ) t , y = − 4.9 t 2 + ( 20 sin θ ) and obtain the values of x and y as shown below. x = ( 20 cos π 6 ) t = ( 10 3 ) t y = − 4.9 t 2 + ( 20 sin π 6 ) t = − 4.9 t 2 + 10 t Use online graphing calculator and draw the graph of x = 10 3 t , y = − 4.9 t 2 + 10 t as shown below in Figure 1. From the Figure 1 it can be noted that the trajectory followed by the projectile is parabolic. Substitute θ = π 4 in x = ( 20 cos θ ) t , y = − 4.9 t 2 + ( 20 sin θ ) and obtain the values of x and y as shown below. x = ( 20 cos π 4 ) t = ( 10 2 ) t y = − 4 (b) To determine To observe: the value of θ that gives the largest distance between the point of launching and point of landing.

Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)

3rd Edition

ISBN: 9780134996684

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 12.1, Problem 66E

(a)

To determine

To graph: The trajectory of a projectile launched from the ground for various values of θ.

(b)

To determine

To observe: the value of θ that gives the largest distance between the point of launching and point of landing.

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Chapter 12.1, Problem 65E

Chapter 12.1, Problem 67E

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Chapter 12 Solutions

Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)

Ch. 12.1 - Identify the graph generated by the parametric...Ch. 12.1 - Prob. 2QC Ch. 12.1 - Describe the curve generated by x = 3 + 2t, y = 12...Ch. 12.1 - Find parametric equations for the line segment...Ch. 12.1 - Use Theorem 12.1 to find the slope of the line x =...Ch. 12.1 - Use the arc length formula to find the length of...Ch. 12.1 - Explain how a pair of parametric equations...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Give parametric equations that generate the line...

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To graph: The trajectory of a projectile launched from the ground for various values of θ .

Solution Summary: The author explains the trajectory of a projectile launched from the ground for various values of theta .

To graph: The trajectory of a projectile launched from the ground for various values of θ.

To observe: the value of θ that gives the largest distance between the point of launching and point of landing.

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