Question

Been stuck for hours


The function H(t) = −16t2 + 90t + 50 shows the height H(t), in feet, of a projectile after t seconds. A second object moves in the air along a path represented by g(t) = 28 + 48.8t, where g(t) is the height, in feet, of the object from the ground at time t seconds.

Part A: Create a table using integers 1 through 4 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)

Part B: Explain what the solution from Part A means in the context of the problem. (4 points)

Answer 1

@mathstudent55

Answer 2

Anybody got an idea? I'm basically just needing help on part A.

Answer 3

Start by evaluating both functions at t = 1, t = 2, t = 3, t = 4

Answer 4

16 90 28 48?

Answer 5

@mathstudent55

Answer 6

How did you get 16?

Answer 7

H(t) = −16t2 + 90t + 50

Let t = 1.

What do you get for H(1) ?

Answer 8

I just found it, idk how i got it, I guessed on it

Answer 9

How do i find h(1)

Answer 10

Like, i'm 100% lost on how I make these, I found some functions but idk how to graph them, can you explain?

Answer 11

H(t) = −16t2 + 90t + 50

To find H(1) you replace t with 1, and you evaluate the expression.

H(1) = -16(1)^2 + 90(1) + 50

Answer 12

H(1) = -16 + 90 + 50 = 124

Now you need H(2).
Replace t with 2 in the H(t) function and evaluate the right side.

H(2) = -16(2^2) + 90(2) + 50

Answer 13

How do I evaluate it? Like how'd you get that

Answer 14

1 is H(1) = -16 + 90 + 50 = 124, I need to solve for 2,3, and 4?

Answer 15

@mathstudent55

Answer 16

I need to find 2,3,4 but how?

Answer 17

Evaluating an expression is just using arithmetic to calculate what it is equal to.

Answer 18

For t = 2, you get

H(2) = -16(2^2) + 90(2) + 50

What is the right side equal to?

Answer 19

H(2) = -16(2v2) + 180 + 50?

Answer 20

If I asked you what is 2 + 2, would you answer 2 + 2, or would you answer 4?

Answer 21

H(2) -16^4 + 230?

Answer 22

good, keep going

Answer 23

H(2) - 64 + 230?

Answer 24

good

Answer 25

H(2) = - 64 + 230?

Answer 26

So it'd be H(2) = 294, or since 64 is negative would it be H(2) = 166?

Answer 27

H(2) = 166

Answer 28

So far we have:

H(1) = 124
H(2) = 166

Now we still need H(3) and H(4) for function H(t)

H(t) = −16t2 + 90t + 50
H(3) = -16(3)^2 + 90(3) + 50

Answer 29

H(3) = -96 + 320

Answer 30

H(3) = 224?

Answer 31

No.
First do 3^2

Answer 32

9

Answer 33

H(3) = -16(3)^2 + 90(3) + 50
H(3) = -16(9) + 90(3) + 50

Now do -16 * 9. You already have 90(3) + 50 = 320

Answer 34

-144

Answer 35

-144 + 270 + 50 right?

Answer 36

yes

Answer 37

H(3)=176?

Answer 38

Correct.
Now we need H(4)
H(4) = -16(4)^2 + 90(4) + 50

Remember to start with 4^2 then multiply that by -16

Answer 39

156?

Answer 40

I got 154

H(4) = -16(4)^2 + 90(4) + 50 = -256 + 360 + 50 =

Answer 41

Ok. We have now function H(t) evaluated at t = 1, t = 2, t = 3, t = 4.

Now we need to do the same for function g(t)

Answer 42

Four more for g(t)?

Answer 43

Alright, what's the functions?

Answer 44

You there math?

Answer 45

The g(t) function is simpler. Just multiply the number (1, 2, 3, 4) by 48.8, then add to 28.
g(t) = 28 + 48.8t
g(1) = 28 + 48.8(1) =
g(1) = 28 + 48.8(2) =
g(1) = 28 + 48.8(3) =
g(1) = 28 + 48.8(4) =

Answer 46

g(1) =76.8
g(2)=125.6
g(3)= 174.4
g(4)= 223.2

Answer 47

Correct. Great job on function g(t).
Now we place all values in a table like part A asks for.