A person standing close to the edge on top of a 96-foot building throws a ball vertically upward. The quadratic function (t) - - 161+ 804 + 96 models the ball's height about the ground, A(t), in feet, e seconds after it was thrown.
a) What is the maximum height of the ball?
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feet
b) How many seconds does it take until the ball hits the ground?
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seconds

196 ft

6 seconds

Step-by-step explanation:

Solution:-

We have a quadratic time dependent model of the ball trajectory which is thrown from the top of a 96-foot building as follows:

The height of the ball is modeled by the distance y ( t ) which changes with time ( t ) following a parabolic trajectory. To determine the maximum height of the ball we will utilize the concepts from " parabolas ".

The vertex of a parabola of the form ( given below ) is defined as:

                    Vertex:

- The modelling constants are: a = -16 , b = 80.

- Now evaluate the given function " y ( t ) " for the vertex coordinate t = 2.5 s. As follows:

The maximum height of the ball is 196 ft at t = 2.5 seconds.

- The amount of time taken by the ball to hit the ground can be determined by solving the given quadratic function of ball's height ( y ( t ) ) for the reference ground value "0". We can express the quadratic equation as follows:

Use the quadratic formula and solve for time ( t ) as follows:

The value of t = -1 is ignored because it lies outside the domain. The ball hits the ground at time t = 6 seconds.