Question

Suppose a toy rocket is launched vertically upward from the top of a building with an initial velocity of 128 feet per second. if air resistance is ignored, the rocket's h height after t seconds is given by the equation h = −16t2 +128t + 100. How long will the rocket's flight last? (to the nearest tenth of a second) A) 7.6 seconds B) 7.9 seconds C) 8.7 seconds D) 9.3 seconds

Answer 1

Option C)

t = 8.7 s

Explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The projectile formula is

h(t) = a*t^2 + v*t + h0

Where,

v = initial vertical velocity of the rocket in feet per second

h0 = initial height of the rocket in feet

h(t) = −16t^2 +128t + 100

If we look at the graph, we can find the point in which the height becomes zero. The value for t at this point will represent the rocket's fight duration

For this problem,

t = 8.717 s