Range of a Projectile We saw in Problem 56 of Exercises 4.2 that if a projec- tile, such as a shot put, is released from a height h, upward at an angle 0 with velocity v, the range R at which it strikes the ground is given by , cose Vo sin@ + Vvž sin°o + 2gh ). R- where g is the acceleration due to gravity. See FIGURE 4.6.4. (a) Show that when h = 0 the range of the projectile is vở sin 20 (b) It can be shown that the maximum range Ru, is achieved when the angle 0 satisfies the equation gh vở + gh" cos 20 Show that maximum range is Vvô+ 2gh R
Range of a Projectile We saw in Problem 56 of Exercises 4.2 that if a projec- tile, such as a shot put, is released from a height h, upward at an angle 0 with velocity v, the range R at which it strikes the ground is given by , cose Vo sin@ + Vvž sin°o + 2gh ). R- where g is the acceleration due to gravity. See FIGURE 4.6.4. (a) Show that when h = 0 the range of the projectile is vở sin 20 (b) It can be shown that the maximum range Ru, is achieved when the angle 0 satisfies the equation gh vở + gh" cos 20 Show that maximum range is Vvô+ 2gh R
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
HELP PLEASE AND ORGANIZE YOUR SOLUTION
AS MUCH AS POSSIBLE PLEASE TYPE YOUR ANSWER THANK UUUU ^^
Transcribed Image Text:16.
75. Range of a Projectile We saw in Problem 56 of Exercises 4.2 that if a projec-
tile, such as a shot put, is released from a height h, upward at an angle 0 with
velocity v, the range R at which it strikes the ground is given by
V, cose
R
Vo sin@ + Vvž sin²0 + 2gh
where g is the acceleration due to gravity. See FIGURE 4.6.4.
(a) Show that whenh = 0 the range of the projectile is
Ground
ở sin 20
FIGURE 4.6.4 Projectile in
Problem 75
(b) It can be shown that the maximum range R, is achieved when the angle 0
satisfies the equation
gh
+ gh
cos 20
Show that maximum range is
vô + 2gh
by using the expressions for R and cos 20 and the half-angle formulas for the
sine and the cosine with / = 20.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning