SOLUTION: The equation h=-16t^-64t+250 (i used the symbol ^ to represent t squared) gives the height of a ball, thrown downward from the top of a 250-ft building with an initial velocity of

Question 473190: The equation h=-16t^-64t+250 (i used the symbol ^ to represent t squared) gives the height of a ball, thrown
downward from the top of a 250-ft building with an initial velocity of 64 ft/s.
Find the time it takes for the ball to reach a height of 100 ft. Round your answer
to the nearest thousandth.
Thank you in advance for your hardwork.

Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The equation h=-16t^-64t+250 (i used the symbol ^ to represent t squared) gives the height of a ball, thrown
downward from the top of a 250-ft building with an initial velocity of 64 ft/s.
Find the time it takes for the ball to reach a height of 100 ft. Round your answer
to the nearest thousandth.
-----------
Use ^2 for squared, ^3 for cubed, etc.
--------------------
h(t) = -16t^2-64t+250 = 100
8t^2 + 32t - 75 = 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=3424 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.65718470958195, -5.65718470958195. Here's your graph:

----------------
t = 1.657 seconds
Ignore the negative answer.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The equation h=-16t^2-64t+250 (i used the symbol ^ to represent t squared) gives the height of a ball, thrown
downward from the top of a 250-ft building with an initial velocity of 64 ft/s.
Find the time it takes for the ball to reach a height of 100 ft. Round your answer to the nearest thousandth.
---
Set the height equal to 100 and solve for "t":
--------
-16t^2-64t+250 = 100
---
-16t^2-64t + 150 = 0
---
Divide thru by -2 to get:
8t^2 + 32t - 75 = 0
-----
Use the quadratic formula to get:
t = 1.657 seconds
=======================
Cheers,
Stan H.
================

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