Explanation Calculation: The vector equation of the path for ideal projectile motion equation is determined as follows, r = ( v 0 cos α t ) i + ( ( v 0 sin α ) t − 1 2 g t 2 ) j Here, v 0 is the projectile’s initial speed, and α is the projectile’s launch angle or firing angle or angle of elevation. From the above equation, the parametric equations are, x = v 0 cos α t And y = ( v 0 sin α ) t − 1 2 g t 2 Here, x is the distance down range, and y is the height of the projectile. Refer to Figure 12.11 in the textbook. If an object is launched from the origin over a horizontal surface with initial speed v 0 and the launch angle α for an ideal projectile motion, then: The projectile’s maximum height is calculated as follows, y max = ( v 0 sin α ) 2 2 g (1) Here, α is projectile’s angle of elevation, g is acceleration due to gravity, which is known as 9.8 m/sec 2 . The projectile’s flight time is calculated as follows, t = 2 v 0 sin α g (2) The projectile’s range is calculated as follows, R = v 0 2 g sin 2 α (3) For example: Find the two angles of elevation enable a projectile to reach a target 15 km downrange on the same level as the gun if the initial speed of the projectile ( v 0 ) is 400 m/sec. Substitute 15 km for R , 400 m/sec for v 0 , and 9.8 m/sec 2 for g in equation (3). 15 km = ( 400 m/sec ) 2 9

Thomas' Calculus Format: Unbound (saleable) With Access Card

14th Edition

ISBN: 9780134768762

Author: Hass, Joel R.^heil, Christopher D.^weir, Maurice D.

Publisher: Prentice Hall

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Chapter 13, Problem 4GYR

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Mention the vector and parametric equations for ideal projectile motion. Also find a projectile’s maximum height, flight time, and range with an examples.

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Thomas' Calculus Format: Unbound (saleable) With Access Card

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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