An archer was practicing target shooting with his bow and arrows when he stops to ponder a calculus problem. The archer learned from physics that if the ground is 5) (vo)²sin (20) flat and we neglect air resistance, then R = where the range, R, is the horizontal distance from the archer to the point where the arrow hits the ground vo represents the initial velocity of the arrow т • g is the acceleration due to gravity (g ~ 32수 ~ 9.81 s2 but just call it g) s2' and 0 is the angle above the horizontal. The archer wonders what initial angle would maximize R. Archer yromnd R а) What does the archer need to find first? Circle one. dR dR dR C) dg dR de A) dvo. B) do D) dt E) dR b) What is an appropriate domain for the objective function (the function to maximize/minimize)? c) Help the archer solve this problem using calculus, in particular derivatives. Show all work and show how you know your answer produces a maximum R.
An archer was practicing target shooting with his bow and arrows when he stops to ponder a calculus problem. The archer learned from physics that if the ground is 5) (vo)²sin (20) flat and we neglect air resistance, then R = where the range, R, is the horizontal distance from the archer to the point where the arrow hits the ground vo represents the initial velocity of the arrow т • g is the acceleration due to gravity (g ~ 32수 ~ 9.81 s2 but just call it g) s2' and 0 is the angle above the horizontal. The archer wonders what initial angle would maximize R. Archer yromnd R а) What does the archer need to find first? Circle one. dR dR dR C) dg dR de A) dvo. B) do D) dt E) dR b) What is an appropriate domain for the objective function (the function to maximize/minimize)? c) Help the archer solve this problem using calculus, in particular derivatives. Show all work and show how you know your answer produces a maximum R.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Transcribed Image Text:5)
An archer was practicing target shooting with his bow and arrows when he stops to
ponder a calculus problem. The archer learned from physics that if the ground is
(vo)²sin (20)
flat and we neglect air resistance, then R
where
g
the range, R, is the horizontal distance from the archer to the point where
the arrow hits the ground
vo represents the initial velocity of the arrow
m
g is the acceleration due to gravity (g
= 32= 9.81
s2
but just call it g)
s2'
and 0 is the angle above the horizontal.
The archer wonders what initial angle would maximize R.
Archer
rund
R
а)
What does the archer need to find first? Circle one.
dR
dR
dR
dR
de
A)
dvo
B)
de
D)
dt
E)
dR
dg
b)
What is an appropriate domain for the objective function (the function to
maximize/minimize)?
Help the archer solve this problem using calculus, in particular derivatives.
Show all work and show how you know your answer produces a maximum R.
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