Tyler kicks a football into the air from a height of 3 feet with an initial vertical velocity of 48 feet per second. Use the vertical motion model, h= -16t^2 + vt + s, where v is the initial velocity in feet per second and s is the height of the football. Round your answer to the nearest tenth if necessary. Maximum height: Feet?

39 feet

Step-by-step explanation:

In this problem, the height of the football at time t is modelled by the equation:

where:

s = 3 ft is the initial height of the ball

v = 48 ft/s is the initial vertical velocity of the ball

is the acceleration due to gravity (downward)

Substituting these values, we can rewrite the expression as

Here we want to find the maximum height reached by the ball.

This is equivalent to find the maximum of the function h(t): the maximum of a function can be found requiring that the first derivative of the function is zero, so

Calculating the derivative of h(t), we find:

And imposing it equal to zero, we find the time t at which this occurs:

And substituting back into h(t), we can find the maximum height of the ball:

idk

step-by-step explanation: