Question

Use the position equation given below, where s represents the height of the object (in feet),
v0
represents the initial velocity of the object (in feet per second),
s0
represents the initial height of the object (in feet), and t represents the time (in seconds), as the model for the problem.
s = −16t2 + v0t + s0
You drop a coin from the top of a building. The building has a height of 1054 feet.
(a) Use the position equation to write a mathematical model for the height of the coin.
s =


(b) Find the height of the coin after 4.5 seconds.
s =
ft

(c) How long does it take the coin to strike the ground? (Round your answer to two decimal places.)
t =
sec

Answer 1

The answers to the questions are

• The mathematical model is given as s = −16t2 + 1054
• The height after 4.5 seconds is 730 feet

• the time it would take to strike the ground is 8.11 seconds.

How to solve for the position of the object

The mathematical model of this problem would be written as

s = −16t2 + v0t + s0

s0 = 1054

then we would have

s = −16t2 + 1054

b. after 4.5 seconds the height is going to be

s = −16t2 + 1054

=  −16(4.5)² + 1054

= -16 * 20.25 + 1054

= 730

C. the time that it takes to strike the ground

s = −16t² + 1054

= 16t² = 1054

t² = 1054/16

= 65.88

t = √65.88

t = 8.11

Hence the time it would take to strike the ground is 8.11 seconds.

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