Question

When a baseball is thrown upward, its height h, in feet, is the function of time t, in seconds. If this function is described by the formula h(t)=-16t^2+24t+5, what is the maximum height of the baseball reaches?

Answer 1

The maximum height of the baseball can be found by determining the vertex of the parabolic function h(t) = -16t^2 + 24t + 5.

The vertex of a parabola in the form of y = ax^2 + bx + c is given by the coordinates (-b/2a, c - b^2/4a).

In this case, a = -16, b = 24, and c = 5.

Therefore, the vertex of the parabola is at t = -b/2a = -24/(2*-16) = 0.75 seconds.

To find the maximum height, we substitute t = 0.75 into the equation for h(t):

h(0.75) = -16(0.75)^2 + 24(0.75) + 5 = 11.5 feet.

Therefore, the maximum height reached by the baseball is 11.5 feet.

Answer 2

the maximal height is 14.75 units of distance.

Explanation:

We want to find the maximum height of the function

h(t) = -16*t^2 + 24*t + 5

In order to find the maximum, we need to find the value of t where the derivate of h(t) is equal to zero, then we evaluate our original function in that time.

The derivate of h(t) (or the vertical velocity) is:

h'(t) = 2*(-16)*t + 24 = -32*t + 24

we want to find the value of such:

0 = -32*t +24

32*t = 24

t = 24/32 = 0.75

Now we evaluate our height function in that value.

h(0.75) = -16*0.75^2 + 25*0.75 + 5 = 14.75 units