# Calculating Initial speed?

1. Sep 9, 2007

### anglum

Calculating Initial speed????

1. The problem statement, all variables and given/known data

A ball is thrown straight up at ground level passes a height of 80.6m in 5.1s.
The acceleration of gravity is 9.8m/s squared. What was its initial speed? answer in units of m/s

2. Relevant equations

What equation is the correct one to use to calculate this

3. The attempt at a solution

I tried using the formula tup=viy/g

and i also tried doing it as a table.... where i calculated the velocity at 5.1 secs to be 15.804 m/s... by dividing 80.6 by 5.1 seconds....

then by adding( since if i was going ahead in seconds instead of back) 9.8 to that speed at 4.1 secs and gettin 25.604 m/s since
and goin up thru till 0 seconds.... to get velocity of 65.784

2. Sep 9, 2007

### learningphysics

80.6 is not the maximum height. There's a kinematics equation you can use directly and solve for v1. Think about the equations you have at your disposal.

3. Sep 9, 2007

### anglum

i know 80.6 is not the maximum height but im guessin i cannto use the subtracting gravity from speed.... so there is just one kinematics equation that i can use and plug in the data i have that will help me solve this

4. Sep 9, 2007

### learningphysics

What is the equation you can use?

5. Sep 9, 2007

### anglum

im not sure what equation i can use which i would plug in the 5.1 seconds and the 80.6m as well as the acceleration of gravity to get my initial speed... tehre is one that i can put all 3 into?

6. Sep 9, 2007

### learningphysics

Yup there is. what are your displacement formulas?

7. Sep 9, 2007

### anglum

what displacement formula lets me take into account gravity

8. Sep 9, 2007

### anglum

so would the formula be

Vf=Vi + at

where i solve for Vf as 80.6/5.1? and plug the gravity into the equation for the value of A?

9. Sep 9, 2007

### learningphysics

No it's a formula that has d... displacement

10. Sep 9, 2007

### anglum

would it be..... Vf squared = Vi squared + 2 A D

where Vf is equal to 80.6/5.1

A = -9.8m/s

D = 80.6 m

?

11. Sep 9, 2007

### learningphysics

Not that equation. The equation has vi, d, t and a. No vf.

12. Sep 9, 2007

### anglum

damn i thought that was the it...

ok so my only other equation that i think is

D = (Vi t) + 1/2 a t squared

so D would = 80.6

a would equal -9.8

would both the t equal 5.1???

then solve for Vi to get the initial speed?

13. Sep 9, 2007

### learningphysics

exactly.

14. Sep 9, 2007

### anglum

ok however... if i solve for that i get the initial velocity to be negative????

that doesnt make sense

15. Sep 9, 2007

### anglum

i get 80.6 = Vi(5.1) + 1/2(-9.8 * 5.1) squared

then i get

80.6 = Vi(5.1) + 1/2(-49.980) squared
80.6=Vi(5.1) + 1/2(2498.00)
80.6=Vi(5.1) + 1249
-1168.400 = Vi(5.1)
-229.098 = Vi

that does not seem right to me

16. Sep 9, 2007

### learningphysics

It should be:
$$\frac{1}{2}gt^2$$

not
$$\frac{1}{2}(gt)^2$$

only t is squared. not g.

17. Sep 9, 2007

### anglum

or do i only square the time and nto the acceleration of gravity?

18. Sep 9, 2007

### anglum

o sorry u posted faster that i typed that question

so is it (1/2g)(t squared)???

19. Sep 9, 2007

### learningphysics

yup.

20. Sep 9, 2007

### anglum

so would the initial speed be equal to 40.794m/s in this particular problem