Final answer:
The maximum height attained by a projectile launched with an initial velocity of 256 ft/s from a 60-foot stage, neglecting air resistance, is 2108 ft.
Step-by-step explanation:
The question involves calculating the maximum height attained by a projectile launched upward. To find this, we can use kinematic equations for projectile motion, taking into account that up is the positive direction, initial velocity is positive, and acceleration due to gravity is negative. Considering the vertical component of the initial velocity, with air resistance neglected, we can calculate the maximum height. The formula for maximum height (h) when projected upward from an initial height (h0) with initial velocity (v0) and gravity (g) is given by:
h = h0 + (v02)/(2g)
In this case, h0 = 60 ft (initial height), v0 = 256 ft/s (initial velocity), and g = 32 ft/s2 (acceleration due to gravity).
Inserting the values into the formula, we get:
Maximum height h = 60 ft + (256 ft/s)2 / (2 * 32 ft/s2)
Maximum height h = 60 ft + 2048 ft
Therefore, the maximum height attained by the projectile is 2108 ft.