If an object is projected upward from ground level with an initial velocity of 128 ft per sec, then it's height in feet after t seconds is given by s(t)=-16t^2+128t. Find the number of seconds it will take to reach its maximum height. What is this maximum height ?
Accepted Solution
A:
Answer: t= 4 secondsMaximum height = 256 feetStep-by-step explanation:The height of the object projected upwards after t seconds is given bys(t)=-16t^2+128t.The expression is a quadratic equation. When this equation is plotted on a graph, height against time, it takes the shape of a parabola whose vertex represents the maximum height attained by the object. To get the value of t at the maximum height,t = -b/2aFrom the equation,a = -16b = 128t = -128/-2×-16= -128 /- 32= 4it will take 4 seconds to reach its maximum heightTo find maximum height attained, put t= 4 in the equations(t)=-16t^2+128tS = -16× 4^2 + 128×4S = -256+512S = 256 feet