44. 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. After how many seconds does the ball attain its maximum height? A.2.87 sec B.3.44 sec C.4.65 sec D.5.41 sec
Option B Solution: It is launched vertically with an initial speed of 110 ft/sec. It will reach maximum height when the speed drops to 0. Vo = 110 feet per second ho = 2 feet So, h(t) = -16t^2 +110t +2 Take the derivative: h'(t) = 110 -32t The maximum height will be at the inflection when the derivative crosses the x-axis, then h'(t)=0. So, set h'(t)=0 and solve for t: 0 = 110 -32t -110 = -32t t = 3.4375 t = 3.44 seconds.
