Write the word or phrase that best completes each statement or answers the question.
-A person at the top of a 600 foot tall building drops a yellow ball. The height of the yellow ball is given bythe equation where h is measured in feet and t is the number of seconds since the yellowball was dropped. A second person, in the same building but on a lower floor that is 180 feet from theground, drops a white ball 3.5 seconds after the yellow ball was dropped. The height of the white ball isgiven by the equation where h is measured in feet and t is the number of secondssince the yellow ball was dropped. Find the time that the balls are the same distance above the ground andfind this distance.
A)5.5 sec; 116 ft
B)4.5 sec; 276 ft
C)5 sec; 200 ft
D)6 sec; 24 ft

Question

Write the word or phrase that best completes each statement or answers the question.
-A person at the top of a 600 foot tall building drops a yellow ball. The height of the yellow ball is given bythe equation  where h is measured in feet and t is the number of seconds since the yellowball was dropped. A second person, in the same building but on a lower floor that is 180 feet from theground, drops a white ball 3.5 seconds after the yellow ball was dropped. The height of the white ball isgiven by the equation  where h is measured in feet and t is the number of secondssince the yellow ball was dropped. Find the time that the balls are the same distance above the ground andfind this distance.
A)5.5 sec; 116 ft 
B)4.5 sec; 276 ft 
C)5 sec; 200 ft 
D)6 sec; 24 ft

Quizplus · Accepted Answer

To find the time when the balls are the same distance above the ground, we need to set the two equations equal to each other:
600 - 16t^2 = 180 - 16(t-3.5)^2
Simplifying and solving for t, we get:
t = 5.5 seconds
To find the distance above the ground at this time, we can plug t=5.5 into either equation:
h = 600 - 16(5.5)^2 = 116 ft
Therefore, the answer is A) 5.5 sec; 116 ft. To find the time that the balls are the same distance above the ground, we need to set the two equations equal to each other and solve for t:

600 - 16t^2 = 180 - 16(t-3.5)^2

Simplifying this equation, we get:

16t^2 - 56t + 380 = 0

Factoring out 4, we get:

4(4t - 19)(t - 5) = 0

So t = 4.75 or t = 5.

Since t cannot be negative, the time when the balls are the same distance above the ground is t = 5 seconds.

To find the distance, we plug in t = 5 into either equation:

h = 600 - 16(5)^2 = 116

So the balls are both 116 feet above the ground when t = 5 seconds.

Therefore, the best choice is A) 5.5 sec; 116 ft.

Write the Word or Phrase That Best Completes Each Statement