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Phantasy [73]
3 years ago
7

A pumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. The pumpkins height, h, at time t sec

onds can be represented by the equation h(t) = -16t^2+ 72t +24.Find the maximum height of the pumpkin and the time it takes to reach this point.
Mathematics
1 answer:
STALIN [3.7K]3 years ago
8 0

Answer: Maximum height =  105 feet

And, It takes 9/4 seconds to reach that point.

Step-by-step explanation:

Here the given function that shows the height of the pumpkin,

h(t) = -16t^2 + 72t + 24 --------(1)

Where t is the time in second.

Differentiating equation (1) with respect to t,

We get,    h'(t) = -32 t + 72

Again differentiating above equation with respect to t,

We get,   h''(t) = -32

For maximum or minimum,    h'(t) = 0

- 32 t + 72 = 0

32 t = 72

t = \frac{9}{4}

At t = 9/4 , h''(t) = Negative value,

Therefore, At t = 9/4 seconds, h(t) is maximum,

And, the maximum value is,

h(\frac{9}{4} ) = -16(\frac{9}{4})^2 + 72(\frac{9}{4}) + 24

h(\frac{9}{4} ) = -16(\frac{81}{16})+ 72(\frac{9}{4}) + 24

h(\frac{9}{4} ) = -81 + 162 + 24=105

Therefore, the maximum height of the pumpkin is 105 feet at 9/4 seconds

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