SOLUTION: I throw a ball inot the air in a movie theater. I throw it up with an initial velocity of 64 feet/scecond froam a balcony 10 feet high. The ceiling of the theater is 58 feet high.

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Question 268960: I throw a ball inot the air in a movie theater. I throw it up with an initial velocity of 64 feet/scecond froam a balcony 10 feet high. The ceiling of the theater is 58 feet high. When will the ball hit the ceiling/
Found 3 solutions by psbhowmick, Alan3354, stanbon:
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Height of ceiling from balcony, h = 58 - 10 = 48 ft.
Upward velocity of the ball while throwing, u = 64 ft/sec.
Acceleration due to gravity, g = 32 ft/sē.

The equation of motion is h = ut - (1/2)gtē.
48 = 64t - (1/2) x 32 x tē
48 = 64t - 16tē
16tē - 64t + 48 = 0
tē - 4t + 3 = 0
(t-3)(t-1) = 0
So either t = 1 or t = 3.

The answer will be the smaller value of 't' when the ball will hit the ceiling so t = 1.

Ans. The ball will hit the ceiling after 1 second from the time of its throwing.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I throw a ball inot the air in a movie theater. I throw it up with an initial velocity of 64 feet/scecond froam a balcony 10 feet high. The ceiling of the theater is 58 feet high. When will the ball hit the ceiling/
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h(t) = -16t^2 + 64t + 10 (t in seconds, h in feet
58 = -16t^2 + 64t + 10
-16t^2 + 64t - 48 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B64x%2B-48+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2864%29%5E2-4%2A-16%2A-48=1024.

Discriminant d=1024 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-64%2B-sqrt%28+1024+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2864%29%2Bsqrt%28+1024+%29%29%2F2%5C-16+=+1
x%5B2%5D+=+%28-%2864%29-sqrt%28+1024+%29%29%2F2%5C-16+=+3

Quadratic expression -16x%5E2%2B64x%2B-48 can be factored:
-16x%5E2%2B64x%2B-48+=+%28x-1%29%2A%28x-3%29
Again, the answer is: 1, 3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B64%2Ax%2B-48+%29

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At t = 1 second. The graph shows the height of the ball if there is nothing in its way.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I throw a ball into the air in a movie theater. I throw it up with an initial velocity of 64 feet/sec1024ond from a balcony 10 feet high. The ceiling of the theater is 58 feet high. When will the ball hit the ceiling/
000000000000000000
Height of the ball is h(t) = -16t^2+vot+so
where vo is the initial velocity and so is the initial height.
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Your Problem:
Solve 58 = -16t^2+64t+10
Rearrange:
16t^2 - 64t + 48 = 0
---
Factor:
16(t^2-4t + 3) = 0
16(t-3)(t-1) = 0
---
Smaller positive solution:
t = 1 second
The ball will hit the ceiling in one second.
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Cheers,
Stan H.