# A catapult launches a boulder with an upward velocity of 184 ft/s. The height of the boulder (h) in feet after t seconds is given by the function h= -16t^2 + 184t + 20. How long does it take the boulder to reach its maximum height? What is the boulder's maximum hieght

2 months ago

## Solution 1

Guest #3523
2 months ago
For this case we have the following equation:
h = -16t ^ 2 + 184t + 20
Deriving we have:
h '= -32t + 184
We equal zero and clear t:
-32t + 184 = 0
32t = 184
t = 184/32
t = 5.75 s
Then, the maximum height is given by:
h (5.75) = -16 * (5.75) ^ 2 + 184 * (5.75) + 20
h (5.75) = 549 feet

It takes the boulder to reach its maximum height about:

t = 5.75 s

the boulder's maximum hieght is:

h (5.75) = 549 feet

Guest #3524
2 months ago

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A ball is thrown into the air with an upward velocity of 32 ft/s. Its height (h) in feet after t seconds is given by the function h= -16t^2 + 32t + 6. How long does it take the ball to reach its maximum height? What is the ball’s maximum height? Roun
Solution 1
For this case we have the following equation:
h = -16t ^ 2 + 32t + 6
Deriving we have:
h '= -32t + 32
We equal zero and clear t:
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The ball's maximum height is:

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Simplify the following expression.
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Solution 2

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The grid shows a section of the beach in Coast City where each square has sides that are 100 yards long.

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This would be a 90° arc.

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