Solve the problem.
-A person at the top of a 600 foot tall building drops a yellow ball. The height of the yellow ball is given by the equation where h is measured in feet and t is the number of seconds since the yellow ball was
Dropped. A second person, in the same building but on a lower floor that is 312 feet from the ground, drops a
White ball 3 seconds after the yellow ball was dropped. The height of the white ball is given by the equation where h is measured in feet and t is the number of seconds since the yellow ball was
Dropped. Find the time that the balls are the same distance above the ground and find this distance.
A) 4.5 sec; 276 ft
B) 4 sec; 344 ft
C) 5 sec; 200 ft
D) 3.5 sec; 404 ft

Question

Solve the problem.
-A person at the top of a 600 foot tall building drops a yellow ball. The height of the yellow ball is given by the equation  where h is measured in feet and t is the number of seconds since the yellow ball was
Dropped. A second person, in the same building but on a lower floor that is 312 feet from the ground, drops a
White ball 3 seconds after the yellow ball was dropped. The height of the white ball is given by the equation  where h is measured in feet and t is the number of seconds since the yellow ball was
Dropped. Find the time that the balls are the same distance above the ground and find this distance.
A) 4.5 sec; 276 ft 
B) 4 sec; 344 ft 
C) 5 sec; 200 ft 
D) 3.5 sec; 404 ft

Quizplus · Accepted Answer

We want to find when the height of the yellow ball is equal to the height of the white ball. Set the two equations equal to each other:

600-16t^2 = 312-16(t-3)^2

Simplify and solve for t:

288 = 32t - 48

336 = 32t

t = 10.5

But we need to subtract 3 seconds since the white ball was dropped 3 seconds after the yellow ball:

t = 7.5

Now plug in t to either equation to find the height:

Yellow ball: h = 600-16(7.5)^2 = 276 ft 
White ball: h = 312-16(4.5)^2 = 276 ft

Thus, the time the balls are the same distance above the ground is 7.5 seconds and the distance is 276 feet.

Solve the Problem. -A Person at the Top of a 600 Foot Tall