MATH SOLVE

4 months ago

Q:
# 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

Accepted Solution

A:

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

Answer:

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

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

Answer:

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