11 The height h of a projectile fired vertically can be mode

11. The height h of a projectile fired vertically can be modeled by the equation h(t) =-16t2 + 128t + 162, where h is the height of the projectile in feet and t is time in seconds. Determine the maximum height of the projectile. A. 162 feet B 256 feet C. 418 feet D. 128 feet E. 1234 feet

Solution

h(t) = -16t^2 + 128*t + 162

For maximum height ====> dh/dt = 0 = -32t + 128 =====> 128 = 32t =====> t = 128/32 = 4

Then maximum height = h(4) = -16*4^2 + 128*4 + 162 = 418 feet (Option C)