Introduction to Calculus in Physics: Calculus is a powerful tool used in all areas of physics. One of the initial applications areas is classical physics, particularly Newtonian mechanics. An important function is the position function s (t) that measures how far the object is from point 0 at time t. The question below deals with just the position function s (t) Problem Set question: The position function for a falling objects is given by s (t) = -16t + vot + s0, where s (t) is the height of the object in feet, vo is the initial velocity, so is the initial height, and t is the time in seconds. A ball is shot upwards from the surface of the earth (so = 0) with an initial velocity of 50 feet per second. What is the maximum height reached by the ball? Round your answer to the nearest integer. The maximum height reached by the ball is Number Units

Introduction to Calculus in Physics: Calculus is a powerful tool used in all areas of physics. One of the initial applications areas is classical physics, particularly Newtonian mechanics. An important function is the position function s (t) that measures how far the object is from point 0 at time t. The question below deals with just the position function s (t) Problem Set question: The position function for a falling objects is given by s (t) = -16t + vot + s0, where s (t) is the height of the object in feet, vo is the initial velocity, so is the initial height, and t is the time in seconds. A ball is shot upwards from the surface of the earth (so = 0) with an initial velocity of 50 feet per second. What is the maximum height reached by the ball? Round your answer to the nearest integer. The maximum height reached by the ball is Number Units

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.2: Graphs

Problem 23E: Magazine Circulation: The circulation C of a certain magazine as a function of time t is given by...

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The Doppler Effect As a train moves toward an observer (see the figure), the pitch of its whistle sounds higher to the observer than it would if the train were at rest, because the crests Of the sound waves are closer together. 'This phenomenon is called the Doppler effect. The observed pitch P is a function of the speed v of the train and is given by P(v)=poSoSov where PO is the actual pitch of the whistle at the source and So = 332 rn/s is the speed of sound in air. Suppose that a train has a whistle pitched at Po = 440 Hz. the function y = P(v) using a graphing device. How can the vertical asymptote of this function be interpreted physically?
Magazine Circulation: The circulation C of a certain magazine as a function of time t is given by the formula C=5.20.1+0.3t Here C is measured in thousands, and t is measured in years since the beginning of 2006, when the magazine was started. a. Make a graph of C versus t covering the first 6 years of the magazines existence. b. Express using functional notation the circulation of the magazine 18 months after it was started, and then find that value. c. Over what time interval is the graph of C concave up? Explain your answer in practical terms. d. At what time was the circulation increasing the fastest?. e. Determine the limiting value for C. Explain your answer in practical terms.
Sales Growth In this exercise, we develop a model for the growth rate G, in thousands of dollars per year, in sales of the product as a function of the sales level s, in thousands of dollars. The model assumes that there is a limit to the total amount of sales that can be attained. In this situation, we use the term unattained sales for difference this limit and the current sales level. For example, if we expect sales grow to 3 thousand dollars in the long run, then 3-s is the unattained sales. The model states that the growth rate G is proportional to the product of the sales level s, and the unattained sales. Assume that the constant of proportionality is 0.3 and that the sales grow to 2 thousand dollars in the long run. a.Find the formula for unattained sales. b.Write an equation that shows the proportionality relation for G. c.On the basis of the equation from the part b, make a graph of G as a function of s. d.At what sales level is the growth rate as large as possible? e.What is the largest possible growth rate?
Radius of a Shock Wave An explosion produces a spherical shock wave whose radius R expands rapidly. The rate of expansion depends on the energy E of the explosion and the elapsed time t since the explosion. For many explosions, the relation is approximated closely by R=4.16E0.2t0.4. Here R is the radius in centimeters, E is the energy in ergs, and t is the elapsed time in seconds. The relation is valid only for very brief periods of time, perhaps a second or so in duration. a. An explosion of 50 pounds of TNT produces an energy of about 1015 ergs. See Figure 2.71. How long is required for the shock wave to reach a point 40 meters 4000 centimeters away? b. A nuclear explosion releases much more energy than conventional explosions. A small nuclear device of yield 1 kiloton releases approximately 91020 ergs. How long would it take for the shock wave from such an explosion to reach a point 40 meters away? c. The shock wave from a certain explosion reaches a point 50 meters away in 1.2 seconds. How much energy was released by the explosion? The values of E in parts a and b may help you set an appropriate window. Note: In 1947, the government released film of the first nuclear explosion in 1945, but the yield of the explosion remained classified. Sir Geoffrey Taylor used the film to determine the rate of expansion of the shock wave and so was able to publish a scientific paper concluding correctly that the yield was in the 20-kiloton range.