Chapter 9.2, Problem 81E

To determine

To Find : Number of feet will the object fall in 7 seconds .

Answer to Problem 81E

784 fts

Explanation of Solution

Given:An object with negligible air resistance is dropped from the top of the willis tower in Chicago at the height of 1450 ft. During the first second of fall , the object falls 16 ft, during the second second , it falls 48 ft , during the third second , it falls 112 feet . If this arithmetic pattern continues , then how many feet will the object fall in 7 seconds .

FORMULA USED :

  $\begin{array}{l}{a}_n=a+(n-1)d\text{nth term formula }\\ \text{or }\\ a_n=dn+c\end{array}$

The given is $\begin{array}{l}{a}_1=16,a_2=48,a_3=80,a_4=112\\ \end{array}$

  $\begin{array}{l}{a}_1=16,a_2=48,a_3=80,a_4=112\\ d=a_2-a_1=48-16=32\\ d=a_3-a_2=80-48=32\\ d=a_4-a_3=112-80=32\end{array}$

Since , the difference is same therefore ,

The series is in arithmetic pattern

Now ,

  $\begin{array}{l}{a}_n=dn+c\\ a_n=32n+c\\ c=a_1-d\\ c=16-32\\ c=-16\\ a_n=32n-16\\ thus\\ \text{Distance = }{\displaystyle \sum _{n=1}^7(32n-16)=784ft}\end{array}$

Hence , The object will fall 784 feet in 7 seconds .