Chapter 11.2, Problem 62PPS

To determine

Find the total distance the object will fall in 10 seconds.

Answer to Problem 62PPS

The object will fall 304feet in 10 seconds.

Explanation of Solution

Given:

When an object is in free fall and air resistance is ignored, it falls 16 feet in the first second, an additional 48 feet during the next second, and 80 feet during the third second. How many total feet will the object fall in 10 seconds?

Concept Used:

This is an arithmetic sequence, so a number of feet is added on to her fall for each second that she is in the air. This number, also known as the common difference is 32 feet.

We can use the formula  $a_n=a_1+(n-1)·d$ to represent the distance she falls on every second after n seconds.

Calculation:

  $a_1=16,n=10,d=32,\text{Find}{a}_{10}$

  $\begin{array}{l}{a}_1=16,n=10,d=32,\text{Find}{a}_{10}\\ a_n=a_1+(n-1)·d\\ a_{10}=16+(10-1)·32\\ a_{10}=16+9·32\\ a_{10}=16+288=304\end{array}$

Thus, the object will fall 304feet in 10 seconds.