2 Part Algebra 1 Question

Question

Use the information to answer the following questions.

The function g(t) = -16t² + vt + h represents the height of an object, g, in feet above the ground in relation to the time, t, in seconds, since the object was thrown into the air with an initial velocity of v feet per second at an initial height of h feet.

A model rocket is launched off the ground at an initial velocity of 80 feet per second.

Part A: Write a function that can be used to describe the flight of the model rocket.

1. A.g(t) = -16t² + t + 80
2. B.g(t) = -16t² + 80
3. C.g(t) = -16t² + 80t + 80
4. D. g(t) = -16t² + 80t

Part B: What domain makes sense for the function in this context?

1. A.all real numbers
2. B.0 ≤ t ≤ 100
3. C.0 ≤ t ≤ 5
4. D. all positive numbers

Answer 1

Hi Haley,

g(t) = -16t² + vt + h

A model rocket is launched off the ground at an initial velocity of 80 feet per second.

Part A:

We know that initial velocity = v = 80 ft/sec and that initial height = h = off the ground = 0 ft. So

g(t) = -16t² + vt + h

g(t) = -16t² + 80t + 0

g(t) = -16t² + 80t, answer D is correct

Part B:

When thinking about domain, we think about what numbers for t make sense. We want to find the function's zeros. Zeros occurs at x = 0 and x = 5. Therefore the domain is C. 0 < = t < = 5

We can also think of this in the context of the problem. In this case, we are modeling an object's height over a period of time. Time only moves forward, "negative time" does not exist. Therefore it would not be possible to have a t less than 0 seconds. Since we are modeling the flight of an object thrown in the air, there will be a time that the object comes back down to the ground. By finding the functions zeros we see that occurs at t = 5 seconds.