Problema Solution
A toy rocket is shot vertically into the air from a launch pad 5 feet above the ground with an initial velocity of 144 feet per second. The height h, in feet, of the rocket above the ground a t seconds after launch is given by the function h(t)= -16t^2+144t+5. How long will it take the rocket to reach its maximum height? What is the maximum height?
Answer provided by our tutors
we need to find the maximum of the parabolic function:
h(t)= -16t^2+144t+5
since the quotient in front of t^2 is -16<0 the function has maximum equal to
h max = c - b^2/(4a)
where a = -16, b = 144, c = 5
h max = 5 - 144^2/(4*(-16))
h max = 329 m is the maximum height.
lets find t, t>0 such that h(t) = 329
by solving -16t^2+144t+5 = 329
we find
t = 4.5 s
click here to see the step by step solution of the equation
it takes 4.5 second for the rocket to reach maximum height.