Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 6, Problem 50CP
You have a great job working at a major league baseball stadium for the summer! At this stadium, the speed of every pitch is measured using a radar gun aimed at the pitcher by an operator behind home plate. The operator has so much experience with this job that he has perfected a technique by which he can make each measurement at the exact instant at which the ball leaves the pitcher’s hand. Your supervisor asks you to construct an algorithm that will provide the speed of the ball as it crosses home plate, 18.3 m from the pitcher, based on the measured speed vi of the ball as it leaves the pitcher’s hand. The speed at home plate will be lower due to the resistive force of the air on the baseball. The vertical motion of the ball is small, so, to a good approximation, we can consider only the horizontal motion of the ball. You begin to develop your algorithm by applying the particle under a net force to the baseball in the horizontal direction. A pitch is measured to have a speed of 40.2 m/s as it leaves the pitcher’s hand. You need to tell your supervisor how fast it was traveling as it crossed home plate. (Hint: Use the chain rule to express acceleration in terms of a derivative with respect to x, and then solve a differential equation for v to find an expression for the speed of the baseball as a function of its position. The function will involve an exponential. Also make use of Table 6.1.)
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Bob has just finished climbing a sheer cliff above a level
beach and wants to figure out how high he climbed. All he
has to use is a baseball, a stopwatch, and a friend on the
ground below with a long measuring tape.
Bob is a pitcher, and knows that the fastest he can throw the
ball is about vo = 32.1 m/s. Bob starts the stopwatch as he
throws the ball, with no way to measure the ball's initial
trajectory, and watches carefully. The ball rises and then falls,
and after ti = 0.710 s the ball is once again level with Bob.
Bob cannot see well enough to time when the ball hits the
ground. Bob's friend then measures that the ball hit the
ground x = 129 m from the base of the cliff.
How high h above the beach was the ball when it
was thrown?
h =
No 1.
x10
TOOLS
X
Bob has just finished climbing a sheer cliff above a beach, and wants to figure out how high he climbed. All he has to use,
however, is a baseball, a stopwatch, and a friend on the beach below with a long measuring tape. Bob is a pitcher and he knows
that the fastest he can throw the ball is about vo = 34.5 m/s. Bob starts the stopwatch as he throws the ball (with no way to
measure the ball's initial trajectory), and watches carefully. The ball rises and then falls, and after t₁ = 0.510 s the ball is once
again level with Bob. Bob cannot see well enough to time when the ball hits the ground. Bob's friend then measures that the ball
landed x = 128 m from the base of the cliff. How high up is Bob, if the ball started exactly 2 m above the edge of the cliff?
2 m
--
X
Bob's position=
x10
TOOLS
m
A Global Positioning System (GPS) receiver is a device that
lets you figure out where you are by receiving timed radio signals from satellites. It
works by measuring the travel time for the signals, which is related to the distance
between you and the satellite. By finding the ranges to several different satellites in
this way, it can pin down your location in three dimensions to within a few meters.
How accurate does the measurement of the time delay have to be in units of
nanoseconds to determine your position to 30 m accuracy? 1s 10^9 ns
Your Answer:
Answer
Chapter 6 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 6.1 - You are riding on a Ferris wheel that is rotating...Ch. 6.2 - A bead slides at constant speed along a curved...Ch. 6.3 - Consider the passenger in the car making a left...Ch. 6.4 - A basketball and a 2-inch-diameter steel ball,...Ch. 6 - In the Bohr model of the hydrogen atom, an...Ch. 6 - Whenever two Apollo astronauts were on the surface...Ch. 6 - A car initially traveling eastward turns north by...Ch. 6 - A curve in a road forms part of a horizontal...Ch. 6 - In a cyclotron (one type of particle accelerator),...Ch. 6 - Why is the following situation impossible? The...
Ch. 6 - You are working during your summer break as an...Ch. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - A 40.0-kg child swings in a swing supported by two...Ch. 6 - Prob. 11PCh. 6 - One end of a cord is fixed and a small 0.500-kg...Ch. 6 - A roller coaster at the Six Flags Great America...Ch. 6 - An object of mass m = 5.00 kg, attached to a...Ch. 6 - A person stands on a scale in an elevator. As the...Ch. 6 - Review. A student, along with her backpack on the...Ch. 6 - A small container of water is placed on a...Ch. 6 - The mass of a sports car is 1 200 kg. The shape of...Ch. 6 - Review. A window washer pulls a rubber squeegee...Ch. 6 - A small piece of Styrofoam packing material is...Ch. 6 - Prob. 21PCh. 6 - Assume the resistive force acting on a speed...Ch. 6 - You can feel a force of air drag on your hand if...Ch. 6 - A car travels clockwise at constant speed around a...Ch. 6 - A string under a tension of 50.0 N is used to...Ch. 6 - Disturbed by speeding cars outside his workplace,...Ch. 6 - A car of mass m passes over a hump in a road that...Ch. 6 - A childs toy consists of a small wedge that has an...Ch. 6 - A seaplane of total mass m lands on a lake with...Ch. 6 - An object of mass m1 = 4.00 kg is tied to an...Ch. 6 - A ball of mass m = 0.275 kg swings in a vertical...Ch. 6 - Why is the following situation impossible? A...Ch. 6 - The pilot of an airplane executes a loop-the-loop...Ch. 6 - A basin surrounding a drain has the shape of a...Ch. 6 - Review. While learning to drive, you arc in a 1...Ch. 6 - A truck is moving with constant acceleration a up...Ch. 6 - Prob. 37APCh. 6 - A puck of mass m1 is tied to a string and allowed...Ch. 6 - Prob. 39APCh. 6 - Members of a skydiving club were given the...Ch. 6 - A car rounds a banked curve as discussed in...Ch. 6 - Prob. 42APCh. 6 - Review. A piece of putty is initially located at...Ch. 6 - A model airplane of mass 0.750 kg flies with a...Ch. 6 - A 9.00-kg object starting from rest falls through...Ch. 6 - For t 0, an object of mass m experiences no force...Ch. 6 - A golfer tees off from a location precisely at i =...Ch. 6 - A single bead can slide with negligible friction...Ch. 6 - Prob. 49CPCh. 6 - You have a great job working at a major league...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Bob has just finished climbing a sheer cliff above a beach and wants to figure out how high he climbed. All he has to use, however, is a baseball, a stopwatch, and a friend on the ground with a long measuring tape. Bob is a pitcher, and knows that the fastest he can throw the ball is ?0=86.0 mph.v0=86.0 mph. Bob starts the stopwatch as he throws the ball (with no way to measure the ball's initial trajectory) and watches carefully. The ball rises and then falls, and after ?1=0.710 s,t1=0.710 s, the ball is once again level with Bob. Bob cannot see well enough to time when the ball hits the ground. Bob's friend then measures that the ball landed a distance of ?=354 ftx=354 ft from the base of the cliff. How high up is Bob if the ball started from exactly 5 ft above the edge of the cliff?arrow_forwardA Global Positioning System (GPS) receiver is a device thatlets you figure out where you are by receiving timed radio signals from satellites. It works by measuring the travel time for the signals, which is related to the distance between you and the satellite. By finding the ranges to several different satellites in this way, it can pin down your location in three dimensions to within a few meters. How accurate does the measurement of the time delay have to be in units of nanoseconds to determine your position to 10 m accuracy? 1 s = 10^9 nsarrow_forwardAccording 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?arrow_forward
- b. The position of a moving particle in vortex is expressed as, x(t) = xo sin(at³ + bt3/2) where xo is the position at t= 0,x (t) is the position at time t, and a and b are the constants. Using dimensional analysis find the units of the constants a and b?arrow_forwardKinesin is a motor protein that moves cargo within cells in a series of rapid 8-nm -long steps. Each step takes 50 μs , and there is an average 15 ms delay between steps. To one significant figure, what is the average speed of a kinesin motor protein? Express your answer to one significant figure and include the appropriate units.arrow_forwardSuppose 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).arrow_forward
- What is the value of n+r/(2.000) 2, written with the correct number of significant figures? O 3.92699 O 3.9269 O 3.9270 O 3.927 O 3.93arrow_forwardThe position-time graph that describes the motion of an object is given as in the figure below. if the values of a= 138.4m, b=227.5m and c=312.5m, Find the distance traveled by the object ( in units of m) over the time interval of [0, 40] s. x(m) a t(s) 10 30 40 Select one: O A. 263.2 OB. 401.6 OC. 490.7 OD. 678.4 O E. 540.0 20arrow_forwardModeling with periodic functions. A Ferris wheel is 30 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. A model for this situation can be represented by the (플) function h(t) - 15 cos + 16 . How many minutes of the ride are spent higher than 21 meters above the ground? Note: If your calculated answer is a decimal, give no more than 2 decimal places in your answer. minutesarrow_forward
- I'm having a hard time figuring out which equation I need to be using to plug in the data into the table. Help!arrow_forwardKinesin is a motor protein that moves cargo within cells in a series of rapid 8-nm-long steps. Each step takes 50 μs, and there is an average 15 ms delay between steps. To one significant figure, what is the average speed of a Kinesin motor protein? TYIA:)arrow_forward1. 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?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Physics for Scientists and Engineers, Technology ...
Physics
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Relative Velocity - Basic Introduction; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=_39hCnqbNXM;License: Standard YouTube License, CC-BY