To determine Verify that the points in the plane that provide the maximum heights of these parabolic trajectories all lie on the given ellipse. Explanation Given information: Refer to the given figure in the textbook for the ellipse with a parabolic trajectory. Calculation: Consider that the expression for the maximum height. y = ( v 0 sin α ) 2 2 g (1) The range at which the maximum height in Equation (1) occurs as, x = v 0 2 2 g sin 2 α = v 0 2 2 g 2 sin α cos α { ∵ sin 2 α = 2 sin α cos α } x = v 0 2 sin α cos α g (2) Consider that equations (1) and (2) describe parametrically the points on a curve in the xy -plane associated with the maximum heights on parabolic trajectories in terms of the parameter α that is launch angle. Square on both sides on the Equation (2). x 2 = ( v 0 2 sin α cos α g ) 2 = v 0 4 sin 2 α cos 2 α g 2 = v 0 4 sin 2 α ( 1 − sin 2 α ) g 2 = v 0 4 sin 2 α g 2 − v 0 4 sin 4 α g 2 Re-arrange the equation. x 2 = v 0 2 g [ v 0 2 sin 2 α g ] − v 0 4 sin 4 α g 2 = v 0 2 g [ 2 v 0 2 sin 2 α 2 g ] − 4 v 0 4 sin 4 α 4 g 2 = 2 v 0 2 g [ v 0 2 sin 2 α 2 g ] − 4 [ v 0 2 sin 2 α 2 g ] 2 = 2 v 0 2 g

Thomas' Calculus - MyMathLab Integrated Review

14th Edition

ISBN: 9780134786223

Author: Hass

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 13.2, Problem 34E

To determine

Verify that the points in the plane that provide the maximum heights of these parabolic trajectories all lie on the given ellipse.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.2, Problem 33E

Chapter 13.2, Problem 35E

Students have asked these similar questions

Is the function f(x) shown in the graph below continuous at x = −5? f(x) 7 6 5 4 2 1 0 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 Select the correct answer below: The function f(x) is continuous. ○ The right limit exists. Therefore, the function is continuous. The left limit exists. Therefore, the function is continuous. The function f(x) is discontinuous. ○ We cannot tell if the function is continuous or discontinuous.

4. Evaluate the following integrals. Show your work. a) -x b) f₁²x²/2 + x² dx c) fe³xdx d) [2 cos(5x) dx e) √ 35x6 3+5x7 dx 3 g) reve √ dt h) fx (x-5) 10 dx dt 1+12

Math 2 question. thx

Chapter 13 Solutions

Thomas' Calculus - MyMathLab Integrated Review

Ch. 13.1 - In Exercises 1–4, find the given limits. 1. Ch. 13.1 - In Exercises 1–4, find the given limits. 2. Ch. 13.1 - In Exercises 1–4, find the given limits. 3. Ch. 13.1 - In Exercises 1–4, find the given limits. 4. Ch. 13.1 - Motion in the Plane In Exercises 5–8, r(t) is the...Ch. 13.1 - Motion in the Plane In Exercises 5–8, r(t) is the...Ch. 13.1 - In Exercises 5–8, r(t) is the position of a...Ch. 13.1 - In Exercises 5–8, r(t) is the position of a...Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.