Question

A baseball is thrown upwards from a height of 5 feet with an initial speed of 64 feet per second, and its height h (in feet) from the ground is given by h(t) = 5 + 64t – 16t2 where t is time in seconds. Using a graphing calculator, determine at what time the ball reaches its maximum height.

Answer 1

2 seconds

Explanation:

Given : A baseball is thrown upwards from a height of 5 feet with an initial speed of 64 feet per second, and its height h (in feet) from the ground is given by
`h(t) = 5 + 64t -16t^2` where t is time in seconds.

To Find: Using a graphing calculator, determine at what time the ball reaches its maximum height.

Solution:

Plot the graph of the given equation

Refer the attached graph

So, the given equation is a downward parabola

So, the y coordinate of vertex of the parabola will give its maximum height and x coordinate will given the time at which the ball is at maximum height

So, Vertex = (2,69)

Maximum height = 69 feet

Time to reach maximum height = 2 seconds

Hence it will take 2 seconds to reach its maximum height.

Answer 2

A graphing calculator shows the ball reaches its maximum height of 69 feet at t = 2 seconds.