×
Get Full Access to Calculus: Early Transcendentals - 2 Edition - Chapter 7.4 - Problem 84
Get Full Access to Calculus: Early Transcendentals - 2 Edition - Chapter 7.4 - Problem 84

×

# Solved: Maximum path length of a projectile (Adapted from

ISBN: 9780321947345 167

## Solution for problem 84 Chapter 7.4

Calculus: Early Transcendentals | 2nd Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Calculus: Early Transcendentals | 2nd Edition

4 5 1 363 Reviews
31
4
Problem 84

Maximum path length of a projectile (Adapted from Putnam Exam 1940) A projectile is launched from the ground with an initial speed V at an angle u from the horizontal. Assume that the x-axis is the horizontal ground and y is the height above the ground. Neglecting air resistance and letting g be the acceleration due to gravity, it can be shown that the trajectory of the projectile is given by y = - 1 2 kx2 + ymax, where k = g 1V cos u22 and ymax = 1V sin u22 2g . a. Note that the high point of the trajectory occurs at 10, ymax2. If the projectile is on the ground at 1-a, 02 and 1a, 02, what is a? b. Show that the length of the trajectory (arc length) is 21 a 0 21 + k2x2 dx. c. Evaluate the arc length integral and express your result in terms of V, g, and u. d. For a fixed value of V and g, show that the launch angle u that maximizes the length of the trajectory satisfies 1sin u2 ln 1sec u + tan u2 = 1. e. Use a graphing utility to approximate the optimal launch angle.

Step-by-Step Solution:
Step 1 of 3

ilr i [.0t. L

Step 2 of 3

Step 3 of 3

##### ISBN: 9780321947345

The full step-by-step solution to problem: 84 from chapter: 7.4 was answered by , our top Calculus solution expert on 12/23/17, 04:24PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. The answer to “Maximum path length of a projectile (Adapted from Putnam Exam 1940) A projectile is launched from the ground with an initial speed V at an angle u from the horizontal. Assume that the x-axis is the horizontal ground and y is the height above the ground. Neglecting air resistance and letting g be the acceleration due to gravity, it can be shown that the trajectory of the projectile is given by y = - 1 2 kx2 + ymax, where k = g 1V cos u22 and ymax = 1V sin u22 2g . a. Note that the high point of the trajectory occurs at 10, ymax2. If the projectile is on the ground at 1-a, 02 and 1a, 02, what is a? b. Show that the length of the trajectory (arc length) is 21 a 0 21 + k2x2 dx. c. Evaluate the arc length integral and express your result in terms of V, g, and u. d. For a fixed value of V and g, show that the launch angle u that maximizes the length of the trajectory satisfies 1sin u2 ln 1sec u + tan u2 = 1. e. Use a graphing utility to approximate the optimal launch angle.” is broken down into a number of easy to follow steps, and 202 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 128 chapters, and 9720 solutions. Since the solution to 84 from 7.4 chapter was answered, more than 232 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345.

#### Related chapters

Unlock Textbook Solution