Question

calculus:rectilinear motion
an object is thrown vertically upward from the ground reaches a certain height after 2 sec and returns to the same height on descent, 8 sec later. find its initial velocity and the height in question.

Answer 1

is this right?

Answer 2

The upward line is 2s, and the total curve at the top is 8s - That seems right :)

Answer 3

We want to use the idea that acceleration due to gravity is constant to help us
Do you know if your class prefers feet or meters? We can use either units, but I don't want to do it in a way you haven't seen =/

Answer 4

@jarp0120

Answer 5

feet

Answer 6

and we need to use derivative to find the answer

Answer 7

So an important general law all airborne objects follow is this:

d^2 y/dt^2 = -32.2 ft/s^2

Answer 8

You know the second derivative of height is a constant

Answer 9

so that's that acceleration?

Answer 10

Lets think mostly about the 8 seconds it was highest up first. What do you think the first derivative of its height was when it was at the very top?

Answer 11

The first derivative is velocity.
The second derivative is acceleration
We know the second derivative is constant

Answer 12

oh yes okay

Answer 13

Can you answer my question?

Answer 14

If youre not sure yet, that's ok too, its just kind of a shortcut if you realize it

Answer 15

i don't know

Answer 16

That's ok, lets move forward with the problem a bit and readdress it later, when it comes up. So we have this constant second derivative...But that's not very descriptive.
Can you use it to get an equation for the first derivative?

Answer 17

is the first derivative v=vo-32t?

Answer 18

Yes, that's very well put. :)

Answer 19

So, do you have any ideas how we might find vo?
Its ok if you dont, but if you do they could be useful

Answer 20

i don't really know

Answer 21

Dont worry, even if you cant see a way yet, we can forge ahead blindly and well find something useful eventually :P

Answer 22

thank you

Answer 23

So often when unsure the best thing to do in real life is just fight forward. So lets do that.
We found an equation for velocity. Can you find one for height? (y, or the 0th derivative)

Answer 24

s=vo-16t^2?

Answer 25

s= Vot-16t^2?

Answer 26

@miracrown?

Answer 27

is the length in 2 sec = to the length in 8 sec?

Answer 28

@jarp0120 you said before: s= Vot-16t^2?

That's technically correct...did you have a d0 at first, and replace it with zero?
or an s0, I guess