Final answer:
It will take 1.5 seconds for the ball thrown into the air to reach its maximum height, which is found by setting the velocity function derived from the position function h(t) equal to zero and solving for time.
Step-by-step explanation:
To determine how long it will take for a ball thrown into the air with an initial upward velocity of 48 ft/s to reach its maximum height, described by the function h(t) = -16t^2 + 48t + 4, we look for the time at which the velocity is zero. This occurs at the ball's maximum height, which is the peak of its trajectory. To find this, we need to calculate the derivative of the position function (h(t)) to get the velocity function and then find the time when the velocity is zero.
The derivative of the position function h(t) is the velocity function v(t) = -32t + 48. Set this equal to zero and solve for t to find the time when the velocity is zero:
0 = -32t + 48
t = 48/32
t = 1.5 seconds
Thus, it takes 1.5 seconds for the ball to reach its maximum height.