Question

You visit the tallest building in a city and drop a penny off the edge of the observation deck. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and then it will continue falling at the same rate. How many feet will the penny fall during the 8th second?

384 feet
272 feet
256 feet
240 feet

Answer 1

The distance that an object falls due to gravity is given by the equation:

d = 1/2 * g * t^2

where d is the distance fallen, g is the acceleration due to gravity, and t is the time elapsed.

In this case, we are given that the penny falls 16 feet during the first second, 48 feet during the second second, and 80 feet during the third second. From this, we can see that the penny is falling with a constant acceleration of 32 feet per second per second (since the distance is increasing by 32 feet each second).

To find the distance that the penny falls during the eighth second, we can use the same equation as before, but with a value of t equal to 8 seconds:

d = 1/2 * g * t^2
d = 1/2 * 32 * 8^2
d = 1/2 * 32 * 64
d = 1024 feet

Therefore, the penny will fall 1024 feet during the eighth second.

Answer 2

The penny will fall 240 feet during the 8th second. The correct answer is 240feet.

The given information suggests that the distance fallen follows an arithmetic sequence where the common difference between consecutive terms is constant. In this case, the common difference is:

48feet−16feet=32feet

To find the distance fallen during the 8th second, we can use the formula for the nth term of an arithmetic sequence:

a_n =a_1 +(n−1)⋅d

where:

a_n is the nth term (distance fallen during the nth second), a_1 is the first term (distance fallen during the first second),

n is the number of terms,

d is the common difference between terms.

For the 8th second (n=8), the formula becomes:

a_8 =16+(8−1)⋅32

a _8 =16+7⋅32

a_8 =16+224

a_8 =240feet

Therefore, the penny will fall 240 feet during the 8th second. The correct answer is 240feet.