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.

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)   (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/s�.

The equation of motion is h = ut - (1/2)gt�.
48 = 64t - (1/2) x 32 x t�
48 = 64t - 16t�
16t� - 64t + 48 = 0
t� - 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)   (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/
---------------
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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1024 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1, 3. Here's your graph:

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

Answer by stanbon(75887)   (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.
===========================================
Cheers,
Stan H.
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