Question

For the vertical motion model h(t)=-16t^2+54t+3, identify the maximum height reached by an object and the amount of time the object is in the air before it hits the ground. Round to nearest tenth

Answer 1

The values of the vertical motion modelled by the quadratic function, h(t) = -16·t² + 54·t + 3 of the object are;

The maximum height reached is approximately 48.6 units

The time of flight is approximately 3.4 seconds

What is a quadratic function?

A quadratic function is a polynomial of the form y = a·x² + b·x + c, where the value of a is larger than or lesser than 0

First part;

The function, for the vertical motion, h(t) = -16·t² + 54·t + 3, is a quadratic function;

The maximum height is found by using the equation that gives the value of x at the maximum value, which is presented as follows;

At the maximum point, $x = \dfrac{-b}{2\cdot a}$

From the equation, a = -16, b = 54, c = 3, and x = t, which gives;

$t = \dfrac{-54}{2\times (-16)} = 1.6875$

The maximum height is therefore;

h(1.6875) = -16 × 1.6875² + 54 × 1.6875 + 3 = 48.6

The time the object is in the air is found using the equation;

h(t) = 0 = -16·t² + 54·t + 3

Using the quadratic formula, $x= \dfrac{-b\pm \sqrt{b^2 - 4\cdot a \cdot c} }{2 \cdot a}$, we have;

$t= \dfrac{-54\pm \sqrt{54^2 - 4\times (-16)\times 3} }{2 \times (-16)}=\dfrac{27\pm \sqrt{777} }{16}$

The time of flight is therefore;

$t=\dfrac{27+ \sqrt{777} }{16}\approx 3.4$

The time of flight is 3.4 seconds

Learn more about quadratic functions or equations here:

brainly.com/question/17105224

#SPJ1