Concept explainers
Matching heights A stone is thrown from the edge of a bridge that is 48 ft above the ground with an initial velocity of 32 ft/s. The height of this stone above the ground t seconds after it is thrown is f(t) = −16t2 + 32t + 48. If a second stone is thrown from the ground, then its height above the ground after t seconds is given by g(t) = −16t2 + ν0 t, where ν0 is the initial velocity of the second stone. Determine the value of ν0 such that both stones reach the same high point.
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Calculus: Early Transcendentals, Books a la Carte Plus MyLab Math/MyLab Statistics Student Access Kit (2nd Edition)
Additional Math Textbook Solutions
Precalculus
Precalculus (10th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
- The Skydiver Again When a skydiver jumps from an airplane, her downward velocity, n feet per second, before she opens her parachute is given by = 176 1 0.834t, where t is the number of seconds that have elapsed since she jumped from the airplane. We found earlier that the terminal velocity for the skydiver is 176 feet per second. How long does it take for her to reach 90 of terminal velocity?arrow_forwardNew Equation of Change? The tax liability T in dollars, for a company that has an initial tax liability of 6200 is dTdt=0.02T. Here, t is time in years. What would be the equation of change for the tax liability if the initial tax liability were 7000?arrow_forwardDrug Concentration When a drug is administered orally, it takes some time before the blood concentration reaches its maximum level. After that time, concentration levels decrease. When 500 milligrams of procainamide is administered orally, one model for a particular patient gives blood concentration C, in milligrams per liter, after t hours as C=2.65(e0.2te2t) What is the maximum blood-level concentration, and when does that level occur?arrow_forward
- WaterWater flows into a tank, and a certain part of it drains out through a valve. The volume v in cubic feet of water in the tank at time t satisfies the equation dvdt=5(v/3). If the process continues for a long time, how much water will be in the tank?arrow_forwardHeight of a Ball If a ball is thrown directly upward with a velocity of 40 ft/s, its height (in feet) after t seconds is given by y=40t16t2 . What is the maximum height attained bythe ball?arrow_forwardFlood Control A river is 8 feet above its flood stage. The water is receding at a rate of 3 inches per hour. Write a mathematical model that shows the number of feet above flood stage after t hours. Assuming the water continually recedes at this rate, when will the river be 1 foot above its flood stage?arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage