Question

A baseball is thrown upward from a height of 2 meters with an intial velocity of 10 meters per second . determine its maximum height, using a(t)=-9.8 meters per second as acceleration due to gravity.

Answer 1

Start with acceleration. Integrate that to get a velocity equation, remembering to include the constant of integration, C. Use the starting velocity to solve for C.
Next, integrate the velocity equation to get a position equation, remembering to include the constant of integration, C. Use the starting position to solve for C.
Set your velocity equation equal to 0 and solve for t to determine when the ball stops rising and starts dropping. Plug this t into your position equation to determine how high it gets.

Answer 2

Try it out and ask me any questions you come across.

Answer 3

(v_1)^2= (v_0)^2 + 2a(x_1-x_0)

(v_1)^2 will be 0

Answer 4

is this for a math class or a kinamatics class?

Answer 5

math class

Answer 6

ok listen to smooth then

Answer 7

-9.8t+c

Answer 8

so 10=-9.8t+c?

Answer 9

Right.

Answer 10

At what time? t=0, right?

Answer 11

2=10t+c

Answer 12

yeah it does

Answer 13

im kinda lost now

Answer 14

Sorry, where did 2 = 10t + c come from?
And I'm sorry, my initial instruction was wrong. You don't have to start with an acceleration equation. You can start with the velocity equation you wrote
v(t) = -9.8t + C
Since the initial velocity is 10, that gives
v(0) = 10 = -9.8(0) +C

Answer 15

So C = 10 gives me a better velocity equation:
v(t) = -9.8t + 10
The first thing to do is to integrate that to get position.

Answer 16

(-9.8t^2)/2+10t

Answer 17

Right. Except +C. Use the initial position, that is position when t=0 to solve for C

Answer 18

is c 2

Answer 19

Yes.

Answer 20

Cool, now use the velocity equation to figure out WHEN it gets to the highest spot. Then use the position formula to figure out the height at that time.

Answer 21

(-9.8t^2)/2+10t+2?

Answer 22

Yes. That's your position equation.

Answer 23

how do youuse the velocity equation to figure out when it gets to the highest spot?

Answer 24

The velocity is positive when the ball is going up, and it is negative when the ball is going down. That means that when the ball is at it's highest, the velocity is 0.

Answer 25

v(t) = 0
solve for t

Answer 26

t=10/9.8

Answer 27

Good.

Answer 28

thats the answer?

Answer 29

What was the question? Have you answered the question yet?

Answer 30

(The answer is no. You haven't answered the question yet.)
It asked you how high the ball gets. You figured out when it reaches that height. Which isn't your answer, but it's a necessary middle step.