Flight of a Rocket Suppose a rocket is fired upward from the surface of the earth with an initial velocity v (measured in meters per second). Then the maximum height h (in meters) reached by the rocket is given by the function
where R = 6.4 × 106 m is the radius of the earth and g = 9.8 m/s2 is the acceleration due to gravity. Use a graphing device to draw a graph of the function h. (Note that h and v must both be positive, so the viewing rectangle need not contain negative values.) What does the vertical asymptote represent physically?
To sketch: The graph of maximum height cover by the rocket
Explanation of Solution
The maximum height reached by the rocket is given below by the function,
Where h is the maximum height in meters, v is the initial velocity in meters per second, R is the radius of the earth and the value of it is
Substitute
Sketch the graph of above given rational function where h and v must be positive,
Figure (1)
The vertical asymptotes occur where the denominator is zero and where the function is undefined.
The zeros of denominator of rational function,
Velocity must be positive value so the value of v is 11200.
The vertical asymptote is
Chapter 3 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning