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 the ball after 7 seconds. Average velocity (m/s) Time interval SOLUTION Through experiments carried out four centuries ago. Galileo discovered that the distance fallen by any freely falling body is proportional to the square of the time it has been falling. (This mode for free fall neglects air resistance.) IF the distance fallen aftert seconds is denoted by s(t) and measured in meters. then Galileo's law is expressed by the equation 7stse 73.5 7sts 7.1 69.09 (t)- 4.9 7sts 7.05 7sts 7.0: 68.845 The difficulty in finding the velocity after 7s is that we are dealing with a single instant of time (t= 7), so no time interval is involved. However, we can approximate the desired quantity by computing the average velocity over the brief time interval of a tenth of a second from t -7 tot 7.l 68.649 7sts 7.001 68.6049 Video Example average velocity hange in position time elapsed 7.) -(7) 0.1 Om/s. The table showes 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 cleser to m/s (rounded to ane decimal place). The instantaneous velocity when -7 is defined to be the limiting value of these average velocities over shorter and shorter time periods that start at -7. Thus the (instantaneous) velocity after 7s is the following. (Round your answer to one decimal place.) - m/s
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 the ball after 7 seconds. Average velocity (m/s) Time interval SOLUTION Through experiments carried out four centuries ago. Galileo discovered that the distance fallen by any freely falling body is proportional to the square of the time it has been falling. (This mode for free fall neglects air resistance.) IF the distance fallen aftert seconds is denoted by s(t) and measured in meters. then Galileo's law is expressed by the equation 7stse 73.5 7sts 7.1 69.09 (t)- 4.9 7sts 7.05 7sts 7.0: 68.845 The difficulty in finding the velocity after 7s is that we are dealing with a single instant of time (t= 7), so no time interval is involved. However, we can approximate the desired quantity by computing the average velocity over the brief time interval of a tenth of a second from t -7 tot 7.l 68.649 7sts 7.001 68.6049 Video Example average velocity hange in position time elapsed 7.) -(7) 0.1 Om/s. The table showes 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 cleser to m/s (rounded to ane decimal place). The instantaneous velocity when -7 is defined to be the limiting value of these average velocities over shorter and shorter time periods that start at -7. Thus the (instantaneous) velocity after 7s is the following. (Round your answer to one decimal place.) - m/s
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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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 the ball after 7 seconds.
Time
interval
Average
velocity (m/s)
7sts 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 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 measured in meters, then Galileo's law is expressed by the equation
7sts 7.1
69.09
s(t) = 4.9t.
7sts 7.05
68.845
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 approximate the desired quantity by computing the
7sts 7.01
68.649
average velocity over the brief time interval of a tenth of a second from t = 7 to t = 7.1:
7 sts 7.001
68.6049
change in position
time elapsed
s(7.1) - s(7)
Video Example )
average velocity =
0.1
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
value of these average velocities over shorter and shorter time periods that start att = 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 velocity when t = 7 is defined to be the limiting
v =
m/s
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