7. Physics students drop a basketball from 5 feet above the ground and its height is measured each tenth of a second until it stops bouncing. The height of the basketball, h, is clearly a function of the time, t, since it was dropped. (b) Is the height of the ball a one-to-one function of time? Explain your answer. (a) Sketch the general graph of what you believe this function would look like. + h (ft) 5+ t (sec) REASONINC

7. Physics students drop a basketball from 5 feet above the ground and its height is measured each tenth of a second until it stops bouncing. The height of the basketball, h, is clearly a function of the time, t, since it was dropped. (b) Is the height of the ball a one-to-one function of time? Explain your answer. (a) Sketch the general graph of what you believe this function would look like. + h (ft) 5+ t (sec) REASONINC

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section: Chapter Questions

Problem 69P: A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0...

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After a ball rolls off the edge of a horizontal table at time t = 0, its velocity as a function of time is given by v=1.2i9.8tj where v is in meters per second and t is in seconds. The balls displacement away from the edge of the table, during the time interval of 0.380 s for which the ball is in flight, is given by r=00.3803vdt To perform the integral, you can use the calculus theorem [A+Bf(x)]dx=Adx+Bf(x)dx You can think of the units and unit vectors as constants, represented by A and B. Perform the integration to calculate the displacement of the ball from the edge of the table at 0.380 s.
A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m), (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P1.69. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure 1.69
1. Kenny is climbing the stairs of his apartment building for exercise. Kenny weighs 83 kg. There are 8 steps in each flight and the height of a single step on the staircase is 11 inches. He climbs the flight of stairs in 3.4 seconds. a.) calculate the long-term rate at which stairs can be climbed considering the given information.(how long can be sustained in stair per second) b.) Why does Kenny descend stairs at a faster rate for a nearly unlimited time although very similar forces are exerted descending as they are ascending?(This points to a fundamentally different process for descending versus climbing stairs.)
According to Timothy Treadwell in 2001 "Now, the bears I live with average, the males are on average twelve hundred pounds. They're the largest bears in the world and they've been clocked at 41 [mph] and they've run a hundred meter dash in 5.85 seconds which human on stimulants doesn't even approach. a. Compute the speed of a grizzly bear using Mr. Treadwell's hundred-meter statement. b. Compute the momentum of a grizzly bear using the speed you calculated in part a. and the average mass stated by Mr. Treadwell. c. How fast would a 250 lb man have to run to have the same momentum you calculated in part b? d. How fast would a 4000 lb car have to drive to have the same momentum you calculated in part b?
2 2. A ball is thrown upward from the top of a 6 feet tall platform. The ball is 30 feet off the ground after 1 second and 22 feet off the ground after 2 seconds. The height h above ground is a quadratic function of the time t after the ball is thrown. a) What is the equation that fits this model? b) How long after the ball is thrown will it reach its maximum height? 2 decimals c) What is the maximum height the ball reaches? Answer Answer Answer
Please Answer 2 and 3 only. Thank youuu. 1. Each spring there is a race up 86 floors of the 102-storey Empire State Building in New York City. If you were able to climb 2 steps per second, how long would it take in minutes to reach the 86th floor if each floor is 14 ft high and each step is about 9 inches? 2. In problem above, what was the racer’s speed (or pace) in minute/mile for the race? 3. Find the distance in meters that a mass traveling at 600 cm/s will cover in 0.016 h.
The function Н () gives the height, above the ground, of a point on a spinning wheel. The function A gives the height of a point on a different spinning wheel and is defined by A(t) = 1.6H(41) . Here, t is time in seconds since the wheels started moving. How does the spinning wheel modeled by function A compare to the wheel for H ? Explain how you know.
Elsa?! Bida-bida. In Arendelle, Queen Elsa loves to show magic tricks to the kids and so, sje begins her show by standing on top of Olaf, a snowman that quickly melts the moment she jumps away from it. Olaf stands 1.63 [m] tall. If Elsa jumps directly upward from Olaf's head and takes 1.94 [s] to rwach a maximum height of 5.37 [m] from where Olaf's head was, how long will it take her to reach the ground from the moment she jumps off Olaf's head? O 2.40 [s] O 3.14 [s] O 1.20 [s] O 0.74 [s]
Suppose a machine is invented to measure the amount of knowledge in a student’s head in units called “factoids.” One student is measured at F(t) = t³ − 6t² + 9t factoids at time t, where t is measured in weeks. a. Find the rate at which the student is gaining (or losing) knowledge as a function of time (be sure to give the units). b. During what time between t = 0 and 11 is the student losing knowledge? c. Sketch a graph of the function F(t).
A frustrated office worker throws his laptop out of his business's high- rise office building. The height, h, in meters of the laptop above the ground at t seconds can be modelled by h(t) = 125-5t². a. Determine the average rate of change between the third and fourth second of the laptop's flight. b. Estimate the rate at which the laptop hits the ground.
1. Andrew and Kevin decide to try out the physics ideas that they are learning and take their baseball pitching machine and a baseball to a 96 feet tall local building. Based on what they have learned the height, s(t), of a baseball, thrown straight up with an initial speed of 80 feet per second from a rooftop 96 feet high is s(t)=-16t^2+80t+96 where t is the elapsed time that the baseball is in the air. The baseball that is pitched miss the rooftop on their way down and eventually strike the ground. a) What is the average velocity of a baseball from t=0 to t=2 seconds? b) What is the velocity of the baseball 2 seconds after it is thrown? c) After how many seconds will the velocity of the baseball reach zero? d) What is the velocity of the baseball t seconds after it is thrown? e) What is the velocity of the baseball as it passes the roof top on the way down?
1. In this problem, you will work out the dimensions and units of quantities from equations. This is a very useful method for checking the physical validity of equations. (a) Consider a particle whose position x is given as a function of its speed v by the following equation v = Ce¯x, where b and C are positive constants. Find the units of C and b in the S.I system. Practice Quiz1 (b) Consider a particle velocity v is given as a function of time t by the following equation, v= Aw sin(at) where A, o are positive constants. Find the units of A and in S.I units. 2. A particle is moving in a straight line. The graph denotes the velocity of the particle as a function of time. (a) Draw a graph of the acceleration of the particle as a function of time. Your graph should include the magnitude and sign of the acceleration. (b) Draw a graph of the displacement of the particle as a function of time. The particle starts from x = 0. 10 8 (s/w) A AA 2.6 -8 -10- t (sec)