Question

If an object is dropped from a height of 144 feet, the function h(t)= -16t^2+144 gives the height of the object after t seconds. When will the object hit the ground?
A. 9 s

B. 6 s

C. 1.5 s

D. 3 s

Answer 1

someone please help i'm confused

Answer 2

When it hits the ground, what is its height?

Answer 3

is the answer d

Answer 4

Not what I asked.

Answer 5

0 i think

Answer 6

Then let zero equal h(t), and solve for t.

Answer 7

so the answer is d

Answer 8

because -16*9+144=0

Answer 9

You were correct before. \[h(t)= -16t^2+144=0 \implies 16t^2=144 \implies t^2=9 \implies t=3\]

Answer 10

thanks

Answer 11

Nice work. Do math every day.

Answer 12

thats great

Answer 13

can u walk me through another one please?

Answer 14

Sure.

Answer 15

hold on

Answer 16

A catapult launches a boulder with an upward velocity of 112 ft/s. The height of the boulder, h, in feet after t seconds is given by the function .
How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.

h=-16t^2+112t+30

A. 7 s; 30 ft

B. 3.5 s; 366 ft

C. 3.5 s; 618 ft

D. 3.5 s; 226 ft

Answer 17

OK, this one is a little different from the first. What kind of function is h(t)?

Answer 18

i'm confused

Answer 19

Look at the function. What kind of function is f(x)=ax^2+bx+c?

Answer 20

idk

Answer 21

Quadratic function. You are obviously learning about them, since both of your problems have had them.

Answer 22

Does the graph of h(t) open up or down?

Answer 23

ok

Answer 24

down

Answer 25

Good. Now, since h(t) is the height at a given time, we want the point on that graph where the height is a maximum. Do you understand that from the problem?

Answer 26

no

Answer 27

Note that the two parts of the question are "When is the boulder at maximum height?" and "What is the maximum height?" (paraphrased here....). So, if we think of the graph, it is the vertex of the parabola. Getting it now?

Answer 28

yes

Answer 29

The t value of the max height can be found by using t=(-b/2a) from the quadratic function you have. After substitution, we get t=-112/-32=7/2. Plug 7/2 into the function to get the maximum height. I'll let you do that part now....

Answer 30

I get about 226 feet. On your list of possible answers, that is answer d.

Answer 31

ok thanks