Question

2. If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet

Answer 1

Answer:

a. 8 seconds.

b. 1 second and 7 seconds.

c. 4 seconds.

d. 256 feet.

Step-by-step explanation:

The given function is

$h(t) = -16t^{2}+128t$

The image attached shows the trajectory of the rocket in a height-time graph. Notice that the maxium point reached is (4, 256), which means after 4 seconds, the rocket has a maximum height of 256 feet. (c) and (d)

Additionally, a parabola is symmetrical, which means it takes the same time going up or down, therefore the rocket reaches the ground after 8 seconds. (a)

Now, when the rocket is 112 feet above the ground, we have

$112 = -16t^{2}+128t$

Where we need to solve for $t$

$0 = -16t^{2}+128t-112$

Using a calculator, we have the solutions $x_{1}= 1$ and $x_{2}=7$, which means after 1 second and 7 second, the rocket is 112 feet above the ground. (b)