Consider a projectile launched at a height h feet above the ground and at an angle 0 with the horizontal. If the initial velocity is vo feet per second, the path of the projectile is modeled by the parametric equations x = t(vo cos(0)) and y = h + (v, sin 0)t - 16t2. A rectangular equation for the path of this projectile is y = 7+ x - 0.008x2. (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 (sec(0))2 y = x2 + tan(0)x + h (b) Find h, vo, and 0. (Round your answers to two decimal places.) Vo = (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. 60 50 40 30 20 50 100 150 10 50 100 150 60 50 60 50 40 40 30 30 20 10 20 50 100 150 10 20 40
Consider a projectile launched at a height h feet above the ground and at an angle 0 with the horizontal. If the initial velocity is vo feet per second, the path of the projectile is modeled by the parametric equations x = t(vo cos(0)) and y = h + (v, sin 0)t - 16t2. A rectangular equation for the path of this projectile is y = 7+ x - 0.008x2. (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 (sec(0))2 y = x2 + tan(0)x + h (b) Find h, vo, and 0. (Round your answers to two decimal places.) Vo = (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. 60 50 40 30 20 50 100 150 10 50 100 150 60 50 60 50 40 40 30 30 20 10 20 50 100 150 10 20 40
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Transcribed Image Text:Consider a projectile launched at a height h feet above the ground and at an angle 0 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(vo cos(0)) and y = h + (vo sin 0)t - 16t2.
A rectangular equation for the path of this projectile is y = 7 + x - 0.008x².
(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 (sec(0))2
y =
x² + tan(0)x + h
Vo
(b) Find h, vo, and 0. (Round your answers to two decimal places.)
Vo
%3D
(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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(d) Use a graphing utility to approximate the maximum height of the projectile. (Round your answers to two decimal places.)
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What is the approximate range of the projectile?
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