Question

Please help! Will FAN AND MEDAL!

A ball is thrown vertically upward from the top of a 96‐ft tower, with an initial velocity of 16 ft/sec. Its position function is s(t) = –16t2 + 16t + 96. What is its velocity in ft/sec when it hits the ground?

a. -32
b. -48
c. -60
d. -80

Answer 1

is this for a calculus class?

Answer 2

How do you get from a position function to a velocity function?

Answer 3

Yes calculus honors.

Answer 4

That I do not know

Answer 5

I'm assuming you've learned derivatives yet? or that has yet to come up in the lesson?

Answer 6

To get from a position function to a velocity function, you take the derivative of the velocity function.
if s(t) is position and v(t) is velocity, then
s'(t)=v(t)
Can you take the derivative of s(t) for me?

Answer 7

Yes I just learned about derivatives.

Answer 8

so if s(t) = –16t^2 + 16t + 96, then what is v(t) ?

Answer 9

The derivative of s(t) is -32t+16

Answer 10

so v(t) = -32t+16

Answer 11

if you knew when the object the ground, you can figure out its speed

to figure out when the object hits the ground, solve s(t) = 0 for t

Answer 12

s(t) = –16t^2 + 16t + 96

0 = –16t^2 + 16t + 96 ... plug in s(t) = 0

use the quadratic formula to solve for t

t =??? or t = ???

Answer 13

I got t=-2,3 or I did it another way and replaced all the "t's" with 0 and got 96.

Answer 14

@jim_thompson5910

Answer 15

`replaced all the "t's" with 0 and got 96` that's if you wanted the y intercept. We want the x intercepts in this case

Answer 16

t = -2 or t = 3 are the correct solutions to s(t) = 0

Answer 17

ignore the negative solution because t = -2 makes no sense. You cannot have negative time values

Answer 18

okay so the first way I did correct then. t= -2 or t=3. So then what do I do?

Answer 19

Then why are all the answer choices - numbers?

Answer 20

the only practical t value is t = 3

the rocket will hit the ground at t = 3

now plug t = 3 into the v(t) equation

Answer 21

`Then why are all the answer choices - numbers? `

they are negative to indicate negative velocities

positive velocities are when the object is moving up
negative velocities are when the object is moving down

Answer 22

I got t=1/2 - 3v/32

Answer 23

v(t) = -32t + 16
v(3) = -32(3) + 16 ... plug in t = 3
v(3) = ______________ (fill in the blank)

Answer 24

-80/3

Answer 25

sorry -80

Answer 26

If that is correct can you help me with one more problem? @jim_thompson5910

Answer 27

-80 is the correct answer

Answer 28

ok make a new post and tag me in it

Answer 29

Okay thank you.