The Sears Tower, at 1,451 feet, is one of the tallest structures in the United States. A penny is thrown from the top of the tow

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The Sears Tower, at 1,451 feet, is one of the tallest structures in the United States. A penny is thrown from the top of the tow

er. The height, h, of the penny is recorded after each second, t, in the table. Write an equation for the curve of best fit, then find the approximate height of the penny after 7 seconds.

Mathematics

1 answer:

Leona [12.6K] · Answer 1 · 2026-02-22T05:48:41+03:00

Answer:

The formula representing the penny's height as a function of time is:

$h(t)=1451-16t^2$

After 7 seconds, the height of the penny will reach 667 feet.

Step-by-step explanation:

The penny experiences free fall.

With an initial velocity of zero and an initial height of h(0)=1,451.

Gravity acts as the acceleration, measured as g=32 ft/s^2.

The model can be initiated by analyzing speed:

$dv/dt=-g\\\\v(t)=v_0-gt=-gt$

Then, the height is expressed as:

$dh/dt=v(t)=-gt\\\\h(t)=h_0-\dfrac{gt^2}{2}=1451-\dfrac{32}{2}t^2\\\\\\h(t)=1451-16t^2$

The height of the penny at approximately 7 seconds can be calculated as:

$h(7)=1451-16(7^2)=1451-16*49=1451-784=667$

After 7 seconds, the penny will stand at a height of 667 feet.