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EXAMPLE 3 Suppose that a ball is dropped from the upper observation deck of the CN Tower in Toronto, 450 m above the ground. Find the velocity of Time interval Average velocity (m/s) the ball after 7 seconds. 7

EXAMPLE 3 Suppose that a ball is dropped from the upper observation deck of the CN Tower in Toronto, 450 m above the ground. Find the velocity of Time interval Average velocity (m/s) the ball after 7 seconds. 7

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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EXAMPLE 3 Suppose that a ball is dropped from the upper observation deck of the CN Tower in Toronto, 450 m above the ground. Find the velocity of Time interval Average velocity (m/s) the ball after 7 seconds. 7<t< 8 73.5 SOLUTION Through experiments carried out four centuries ago, Galileo discovered that the distance fallen by any freely falling body is proportional to 7sts7.1 69.09 the square of the time it has been falling. (This model for free fall neglects air resistance.) If the distance fallen after t seconds is denoted by s(t) and 7<t<7.05 68.845 measured in meters, then Galileo's law is expressed by the equation 7<t<7.01 68.649 s(t) = 4.9t?. 7<t<7.001 68.6049 The difficulty in finding the velocity after 7 s is that we are dealing with a single instant of time (t = 7), so no time interval is involved. However, we can Video Example ) approximate the desired quantity by computing the average velocity over the brief time interval of a tenth of a second from t = 7 to t = 7.1: change in position time elapsed s(7.1) – s(7) 0.1 average velocity = - 4.9(O) 4.9 0.1 m/s. The table shows the results of similar calculations of the average velocity over successively smaller time periods. It appears that as we shorten the time period, the average velocity is becoming closer to velocity when t = 7 is defined to be the limiting value of these average velocities over shorter and shorter time periods that start at t = 7. Thus the (instantaneous) velocity after 7 s is the following. (Round your answer to one decimal place.) m/s (rounded to one decimal place). The instantaneous V = m/s
Transcribed Image Text:EXAMPLE 3 Suppose that a ball is dropped from the upper observation deck of the CN Tower in Toronto, 450 m above the ground. Find the velocity of Time interval Average velocity (m/s) the ball after 7 seconds. 7<t< 8 73.5 SOLUTION Through experiments carried out four centuries ago, Galileo discovered that the distance fallen by any freely falling body is proportional to 7sts7.1 69.09 the square of the time it has been falling. (This model for free fall neglects air resistance.) If the distance fallen after t seconds is denoted by s(t) and 7<t<7.05 68.845 measured in meters, then Galileo's law is expressed by the equation 7<t<7.01 68.649 s(t) = 4.9t?. 7<t<7.001 68.6049 The difficulty in finding the velocity after 7 s is that we are dealing with a single instant of time (t = 7), so no time interval is involved. However, we can Video Example ) approximate the desired quantity by computing the average velocity over the brief time interval of a tenth of a second from t = 7 to t = 7.1: change in position time elapsed s(7.1) – s(7) 0.1 average velocity = - 4.9(O) 4.9 0.1 m/s. The table shows the results of similar calculations of the average velocity over successively smaller time periods. It appears that as we shorten the time period, the average velocity is becoming closer to velocity when t = 7 is defined to be the limiting value of these average velocities over shorter and shorter time periods that start at t = 7. Thus the (instantaneous) velocity after 7 s is the following. (Round your answer to one decimal place.) m/s (rounded to one decimal place). The instantaneous V = m/s
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