Question

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 tower. 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.

Answer 1

Answer:

The equation for the height of the penny in function of time is:

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

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

Step-by-step explanation:

The penny will have a free fall.

The initial velocity is zero, and the initial height is h(0)=1,451.

The acceleration will be the gravity, that has a value g=32 ft/s^2.

Then, we can model this starting by the speed:

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

Then, the height becomes:

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

The approximate height of the penny after 7 seconds can be calculated as:

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

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