Question

A person standing cloes to the edge on the top of a 200-foot building throws a baseball vertically upward. The quadratic functions(t)=-16t^2+64t+200models the ball's height above the ground, s(t), in feet, t seconds after it was thrown.A) After how many seconds does the ball reach it's maximum height? What is the maximum height?B) How many seconds does it take until the ball finally hits the ground?C) Find s(0) and describe what this means. D) Use your res ults from parts (a) through (c) to graph the quadratic function . Begin the graph with t = 0 and end with the value oft for which the ball hits the ground.

Answer 1

Part (A): it would take 2 seconds to reach maximum height of 264 foot.

Part (B): Ball will hit the ground in about 6.1 seconds

Part (C): S(0) represents the initial height of the base ball or the baseball was thrown at a height of 200 ft.

Explanation:

Consider the provided function.

`s(t)=-16t^2+64t+200`

Part (A) After how many seconds does the ball reach it's maximum height? What is the maximum height?

The coefficient of t² is a negative number, so the graph of the above function is a downward parabola.

From the given function a=-16, b=64 and c=200

The downward parabola attain the maximum height at the x coordinate of the vertex.
`x=(-b)/(2a)`

Substitute the respectives.

`x=(-64)/(2(-16))=2`

Substitute x=2 in the provided equation.

`s(t)=-16(2)^2+64(2)+200=264`

Hence, it would take 2 seconds to reach maximum height of 264 foot.

Part (B) How many seconds does it take until the ball finally hits the ground?

Substitute s(t)=0 in the provided equation.

`-16t^2+64t+200=0`

Use the formula
`x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)` to find the solutions of the quadratic equation.

`t=(-64+√(64^2-4\left(-16\right)200))/(2\left(-16\right))\\t=\pm(4+√(66))/(2)\\t\approx-2.1\ or\ 6.1`

Reject the negative value as time can't be a negative number.

Hence, ball will hit the ground in about 6.1 seconds

Part (C) Find s(0) and describe what this means.

Substitute x=0 in the provide equation.

`s(0)=-16(0)^2+64(0)+200`

`s(0)=200`

S(0) represents the initial height of the base ball or the baseball was thrown at a height of 200 ft.

Part (D) Use your results from parts (a) through (c) to graph the quadratic function.

Use the starting points (0,200), maximum point (2,264) and the end point (6.1,0) in order to draw the graph of the function.

Connect the points as shown in figure.

The required figure is shown below.