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Algebra 1

7.5.2 A Time-Distance Quadratic Model

Algebra 17.5.2 A Time-Distance Quadratic Model

7.5.2 A Time-Distance Quadratic Model

7.5.2 • A Time-Distance Quadratic Model

Activity

A rock is dropped from the top floor of a 500-foot-tall building. A camera captures the distance the rock traveled, in feet, after each second.

1. How many feet will the rock have fallen after 6 seconds? Be prepared to show your reasoning.

2. Jada noticed that the distances fallen are all multiples of 16. She wrote down: 16=16·116=16·1 64=16·464=16·4 144=16·9144=16·9 256=16·16256=16·16 400=16·25400=16·25

Then, she noticed that 1, 4, 9, 16, and 25 are 1212, 2222, 3232, 4242, 5252.

a. Use Jada’s observations to predict the distance fallen in feet after 7 seconds. (Assume the building is tall enough that an object dropped from the top of it will continue falling for at least 7 seconds.) Be prepared to explain your reasoning.

b. Write an equation for the function, with dd representing the distance dropped after tt seconds.

Self Check

An object is dropped from a building and falls so that the distance in feet it falls, d ( t ) , is found by d ( t ) = 16 t 2 , after t seconds. How many feet has it fallen after 10 seconds?
  1. 2,560
  2. 1,600
  3. 320
  4. 160

Additional Resources

Finding Distance Fallen

The Empire State Building is 1250 ft high (excluding the lightning rod). A visitor drops a penny from the top, and it falls straight down. How far has it fallen after 5 seconds?

Recall the previous activity’s formula h(t)=16t2h(t)=16t2.

Substitute t=5t=5.

h(5)=16(5)2=16·25=400h(5)=16(5)2=16·25=400 feet.

Try it

Finding Distance Fallen

Will the penny dropped from the Empire State Building reach the ground after 9 seconds? Be prepared to show your reasoning.

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