Consider a projectile launched at a height h feet above the ground and at an angle e with the horizontal. If the initial velocity is v, feet per second, the path of the projectile is modeled by the parametric equations x = t(v, cos(0)) and y h+ (v, sin r - 16 A rectangular equation for the path of this projectile is y=5+x-0.008x. (a) Eliminating the parameter t from the position function for the motion of a projectile to shows that the rectangular equation is as follows. -16 (secte)) tan(e)x +h (b) Find h, v and 8. (Round your answers to two decimal places.) (c) Use a graphing utilty to graph the rectangular equation for the path of the projectile. Confirm your answer in part (b) by sketching the curve represented by the parametric equations. 50 40 50 40 30 30 20 20 10 10 50 100 150 20 40 60 80

Advanced Engineering Mathematics
10th Edition
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Consider a projectile launched at a height h feet above the ground and at an angle e with the horizontal. If the initial velocity is v feet per second, the path of the projectile is modeled by the parametric equations x = t(v.
cos(0)) and y h+ (v, sin )t - 16
A rectangular equation for the path of this projectile is y =5+x-0.008x.
(a) Eliminating the parametert from the position function for the motion of a projectile to shows that the rectangular equation is as follows.
-16 (sec(e))2 . tan(e)x +h
(b) Find h, vo and 8. (Round your answers to two decimal places.)
(C) Use a graphing utility to graph the rectangular equation for the path of the projectile. Confirm your answer in part (b) by sketching the curve represented by the parametric equations.
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Transcribed Image Text:Consider a projectile launched at a height h feet above the ground and at an angle e with the horizontal. If the initial velocity is v feet per second, the path of the projectile is modeled by the parametric equations x = t(v. cos(0)) and y h+ (v, sin )t - 16 A rectangular equation for the path of this projectile is y =5+x-0.008x. (a) Eliminating the parametert from the position function for the motion of a projectile to shows that the rectangular equation is as follows. -16 (sec(e))2 . tan(e)x +h (b) Find h, vo and 8. (Round your answers to two decimal places.) (C) Use a graphing utility to graph the rectangular equation for the path of the projectile. Confirm your answer in part (b) by sketching the curve represented by the parametric equations. 50 40 50 40 30 30 20 20 10 10 50 100 150 40 60 80 381 P Type here to search 11:01 PM 4/14/2021
(c) Use a graphing utility to graph the rectangular equation for the path of the projectile. Confirm your answer in part (b) by sketching the cur
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(d) Use a graphing utility to approximate the maximum height of the projectile. (Round your answers to two decimal places.)
ft
What is the approximate range of the projectile?
ft
P Type here to search
梦 S 0=
a
立
Transcribed Image Text:(c) Use a graphing utility to graph the rectangular equation for the path of the projectile. Confirm your answer in part (b) by sketching the cur 50 40 50 40 30 30 20 20 10 10 50 100 150 20 40 60 80 50 40 30 20 50 100 150 10 50 100 150 (d) Use a graphing utility to approximate the maximum height of the projectile. (Round your answers to two decimal places.) ft What is the approximate range of the projectile? ft P Type here to search 梦 S 0= a 立
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