25 POINTSSSS // A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second. What is the maximum height, in feet, the ball will attain?
1st let's calculate the time needed to reach the maximum distance
h(t) = - 1/2 gt² + v₀t + h₀ h(t) = - 1/2 (9.8).t² + 110.t + 2 ; h(t) = -4.9.t² +110.t + 2 The time needed to reach the maximum height is when the derivative of h(t) is equal to 0: h'(t) = 2(-4.9).t + 110 → h'(t) = -9.8.t + 110 = 0 and t = 11.22 seconds Now to find the maximum height reaches, replace t with 11.2 in the equation h(t) = -4.9.t² +110.t + 2
