a rocket is launched from a cliff 30 ft above the ground.

Question

a rocket is launched from a cliff 30 ft above the ground. Its height (h) is feet above the ground and (t) seconds after it is launchers given by the function.

At what two times is the rocket 100 ft. Above the ground?

How many seconds after launch is the rocket 606 ft. Above the ground?

How long does it take the rocket to come back to the ground?

Answer 1

h(t) = -16t^2 + vot + 30 where vo = initial velocity

100 = -16t^2 + vot + 30, solve for t to find when it's 100 feet above ground. It's a quadratic equation, use the quadratic formula, with ax^2 + bx + c, such that x=-b/2a + or - (1/2a)sqr(b^2 - 4ac)

16t^2 - vot+70 = 0 has a=16, b=-vo and c=70

t = vo/32 + or - (1/32)sqr(vo^2 - 4(16)(70))

same method for 606

606 = h(t)

same method for ground level

0 = h(t)