Answer:
a) 64 feet
b) 3 seconds
Step-by-step explanation:
a)
The maximum height of can be bound by finding the y-coordinate of the vertex of
.
Compare this equation to to find the values of
.
.
The x-coordinate of the vertex can be found by evaluating:
So the x-coordinate of the vertex is 1.
The y-coordinate can be found be evaluating at
:
So the maximum height of the rocket is 64 ft high.
b)
When the rocket hit's the ground the height that the rocket will be from the ground is 0 ft.
So we are trying to find the second t such that:
I'm going to divide both sides by -16:
Now we need to find two numbers that multiply to be -3 and add to be -2.
Those numbers are -3 and 1 since (-3)(1)=-3 and (-3)+(1)=-2.
This implies we have either or
The first equation can be solved by adding 3 on both sides: .
The second equation can be solved by subtracting 1 on both sides: .
So when seconds, is when the rocket has hit the ground.