An object is launched directly in the air at a speed of 144 feet per second from a platform located 12 feet in the air. The motion of the object can be modeled using the function f(t)=−16t2+144t+12, where t is the time in seconds and f(t) is the height of the object. When, in seconds, will the object reach its maximum height? Do not include units in your answer.

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princessxriana princessxriana · Answer 1 · 2019-11-04T22:32:05+01:00

Answer:After 2 seconds the object reach its maximum height of 80 feet.

Step-by-step explanation:

Consider the provided function.

The function is a downward parabola.

The object will reach its max height at the vertex of the parabola.

The vertex of the parabola is given by ,

Where the standard form is .

By comparing the provided function with the standard form.

a=-16, b=64 and c=16

Thus, the vertex are:

Now substitute the value of t in the provided function.

Hence, after 2 seconds the object reach its maximum height of 80 feet.

Explanation:

onyebuchinnaji onyebuchinnaji · Answer 2 · 2021-10-05T17:26:38+02:00

The time for the object to reach maximum height is 4.5 s.

The given equation of the object's motion;

f(t) = -16t² + 144t + 12

The time for the object to reach maximum height will occur when the final velocity will be zero.

Velocity is defined as the change in displacement per change in time of motion.

[tex]v = f' = \frac{df(t)}{dt}[/tex]

f' = -32t + 144

When the object reaches maximum height, f' = 0

0 = -32t + 144

32t = 144

[tex]t = \frac{144}{32} \\\\t = 4.5 \ s[/tex]

Thus, the time for the object to reach maximum height is 4.5 s.

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