a. Explanation Given: The position of the object without air is governed by the differential equation s ' ' ( t ) = − g , where g = 9.8 m / s 2 is the acceleration due to gravity. Calculation: Consider the object is fired at time t = 0 and that s ( t ) is the position of the object at time t ≥ 0 . Integrating both sides of the differential equation s ″ ( t ) = − 9.8 gives the velocity v ( t ) . ∫ s ″ ( t ) d t = − ∫ 9.8 d t s ′ ( t ) = − 9.8 t + C 1 Therefore, the velocity is v ( t ) = − 9.8 t + C 1 (1) Use the initial condition v ( 0 ) = 49 to evaluate the constant C 1 . v ( 0 ) = − 9.8 × 0 + C 1 49 = 0 + C 1 49 = C 1 Therefore, the values is C 1 = 49 . Substitute 49 for C 1 in equation (1), v ( t ) = − 9.8 t + 49 . Therefore, the velocity function is v ( t ) = − 9.8 t + 49 . Again integrate both sides of the velocity equation v ( t ) gives the position function s ( t ) . ∫ v ( t ) d t = ∫ ( − 9 b. To determine To find: The time and the height of the object when reached at the point of trajectory.

2nd Edition

ISBN: 9781323178522

Author: Briggs

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter D1.1, Problem 30E

To determine

To find: The position and velocity functions for the object which is above the ground.

To determine

To find: The time and the height of the object when reached at the point of trajectory.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter D1.1, Problem 29E

Chapter D1.1, Problem 31E

Students have asked these similar questions

纟 W₂ Find S-FX SB.MX

4. The revenue (in thousands of dollars) from producing x units of an item is R(x)=8x-0.015 x². a) Find the average rate of change of revenue when the production is increased from 1000 to 1001 units.

MATH 122 WORKSHEET 3 February 5, 2025 . Solve the following problems on a separate sheet. Justify your answers to earn full credit. 1. Let f(x) = x² - 2x + 1. (a) Find the slope of the graph of y = f (x) at the point P = (0,1) by directly evaluating the limit: f'(0) = lim ( f(Ax) - f(0) Ax Ax→0 (b) Find the equation of the tangent line 1 to the graph of ƒ at P. What are the x and y intercepts of 1 ? (c) Find the equation of the line, n, through P that is perpendicular to the tangent line l. (Line n is called the normal line to the graph of f at P.) (d) Sketch a careful graph that displays: the graph of y = f (x), its vertex point, its tangent and normal lines at point P, and the x and y intercepts of these lines. Bonus: Find the coordinates of the second point, Q, (QP), at which the normal line n intersects the graph of f. 2. A rock is thrown vertically upward with an initial velocity of 20 m/s from the edge of a bridge that is 25 meters above a river bed. Based on Newton's Laws of…

Chapter D1 Solutions

CODE/CALC ET 3-HOLE

Ch. D1.1 - Prob. 1E Ch. D1.1 - Prob. 2E Ch. D1.1 - Prob. 3E Ch. D1.1 - If the general solution of a differential equation...Ch. D1.1 - Does the function y(t) = 2t satisfy the...Ch. D1.1 - Does the function y(t) = 6e3t satisfy the initial...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...

Additional Engineering Textbook Solutions

Find more solutions based on key concepts

The inequality 1x3 can be written in interval notation as _______________. (pp. A76-A77)

Precalculus

Fill in each blank so that the resulting statement is true. The quadratic function f(x)=a(xh)2+k,a0, is in ____...

Algebra and Trigonometry (6th Edition)

A box contains 3 marbles: 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking 1 marble f...

A First Course in Probability (10th Edition)

Piston compression A piston is seated at the top of a cylindrical chamber with radius 5 cm when it starts movin...

Calculus: Early Transcendentals (2nd Edition)

x vs. Two symbols are used for the mean: and x. a. Which represents a parameter, and which a statistic? b. In...

Introductory Statistics

Identify f as being linear, quadratic, or neither. If f is quadratic, identify the leading coefficient a and ...

College Algebra with Modeling & Visualization (5th Edition)

Knowledge Booster

Learn more about

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

The position and velocity functions for the object which is above the ground.

Solution Summary: The author explains the position and velocity functions for the object which is above the ground.