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

it would be 2 seconds. the maximum height would be 69 feet in 2 seconds. you can find this by plugging it into your graphing calculator in y=

Answer 2

It will take 2 seconds to reach its maximum height.

Explanation:

We have 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.

We have to find, Using a graphing calculator, determine at what time the ball reaches its maximum height.

Solution:

The equation represented as
`h(t) = 5 + 64t - 16t^2`

Where, t is time in seconds and h is the height.

Now, We plot the graph of the given equation.

Refer the attached graph below.

The given equation is a downward parabola with 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

The vertex of the equation is given by V=(2,69)

Maximum height = 69 feet

Time to reach maximum height = 2 seconds

Therefore, It will take 2 seconds to reach its maximum height.