<img src="https://tex.z-dn.net/?f=f%28x%29%3D16t%5E2%2B32t" id="TexFormula1" title="f(x)=16t^2+32t" alt="f(x)=16t^2+32t" align="

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3 years ago

absmiddle" class="latex-formula">The function f(x)=-16t^2+32t represents the height of a pumpkin t seconds after it is launched from a catapult. When does the pumpkin reach its maximum height? What is the maximum height of the pumpkin?

Mathematics

1 answer:

Nataly_w [17]3 years ago

6 0

Answer:

- time = 1second

- maximum height = 16m

Step-by-step explanation:

Given the height of a pumpkin t seconds after it is launched from a catapult modelled by the equation

f(t)=-16t²+32t... (1)

The pumpkin reaches its maximum height when the velocity is zero.

Velocity = {d(f(x)}/dt = -32t+32

Since v = 0m/s (at maximum height)

-32t+32 = 0

-32t = -32

t = -32/-32

t = 1sec

The pumpkin reaches its maximum height after 1second.

Maximum height of the pumpkin is gotten by substituting t = 1sec into equation (1)

f(1) = -16(1)²+32(1)

f(1) = -16+32

f(1) = 16m

The maximum height of the pumpkin is 16m

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