Answer to Question #162257 in Algebra for Eden G Potter

Question

julian drops a coin from the top of the empire state building, which is approximately 1250 feet tall. if the coin falls 16 feet in the first second, 48 feet the next second, 80 feet the third second, and so on, approximately how long will it take for the coin to hit the ground?

Answer 1

The first term = 16

The second term = 48

The third term = 80

Let the 1^st term be the first second and the 2^nd term be the second term and the 3^rd term be the third second.

The distance to be travelled is 1250 feet.

The multiple of 16 around 1250 feet is 1248 feet or 1264 feet. However, the closest to the distance travelled which was 1250 feet is 1248 feet.

Now we apply the arithmetic sequence as below;

16, 48, 80

a, a+d, a+2d

a=16

a+d=48

a+2d=80

Where

a = is the first term =16

d = is the difference = 32

We are interested in the n^th term which is 1248

And the formula for calculating n^th term is as below;

a_n = a + (n-1)d

1248 = 16 + (n - 1)32

1248 = 16 +32n - 32

1248 = 32n - 16

32n = 1264

n = 1264/32

n = 39.5

Thus it will take approximately 40 seconds for the coin to hit the ground.