Q42. - Algebra 2

Question

To prove that objects of different weights fall at the same rate, Galileo dropped two objects with different weights from the Leaning Tower of Pisa in Italy. The objects hit the ground at the same time. When an object is dropped from a tall building, it falls about 16 feet in the first second, 48 feet in the second second, and 80 feet in the third second, regardless of its weight. How many feet would an object fall in the tenth second?

Step-by-Step Solution

Answer

The object falls 304 feet in tenth second.

Step 1. Given Information.

Given to prove that objects of different weights fall at the same rate, Galileo dropped two objects with different weights from the Leaning Tower of Pisa in Italy. The objects hit the ground at the same time. When an object is dropped from a tall building, it falls about 16 feet in the first second, 48 feet in the second second, and 80 feet in the third second, regardless of its weight.

Step 2. Calculation .

Here the sequence is given by 16, 48, 80, …

The n^th term of an arithmetic sequence is given by $a_n=a_1+(n-1)d$ .

 

Here the first term is  $a_1=16$

The difference between the first two terms is  $48-16=32$

The difference between the next two terms is  $80-48=32$

The common difference is  $d=32$

And the required term is  $n=10$

 Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_{10}=16+(10-1)\left(32\right)\\ a_{10}=16+\left(9\right)\left(32\right)\\ a_{10}=16+288\\ a_{10}=304\end{array}$

Step 3. Conclusion .

Hence, the object falls 304 feet in tenth second.