# Initial velocity

1. May 17, 2010

### Brittykitty

What formula would I use to find the initial velocity?

An object is thrown vertically into the air and reaches a height of 30.0 m. Neglecting air friction, what was the object’s initial velocity?

I dont quite remember how to do this. Is it 30.0m / 9.81[m/s]^2?

2. May 17, 2010

### rock.freak667

There are mainly three equations of motion

$$s= ut+\frac{1}{2}at^2$$

$$v=u+at$$

$$v^2=u^2+2as$$

u= initial velocity
v= final velocity
s= displacement.

Which one has all of the information you need in it? (note: a is acceleration, which is just 'g' in your case)

3. May 17, 2010

### Brittykitty

Hello :)
I'm not given the time so I'm assuming its v^2=u^2+2as ?

4. May 17, 2010

### rock.freak667

Yes, also since the maximum height is given you have the final velocity.

5. May 18, 2010

### Brittykitty

Thank you! :)
one more question, how would I find the initial velocity? Would it be 0? or 9.81[m/s]^2? dont remember that part either :\

6. May 18, 2010

### rock.freak667

Remember m/s2 are the units for acceleration, so in your equation, your acceleration is -9.81.

At the maximum height, the object stops rising. So the final velocity is?

When you understand these two things, using the equation you told me it would be v2=u2+2as, you can can find 'u'.

7. May 18, 2010

### Brittykitty

the final velocity would be (30.0m) (-9.81)?

8. May 18, 2010

### rock.freak667

no, remember the object's goes up, reaches the maximum height and then moves back down to Earth. So during this, the velocity goes from +ve to 'something' (at max) and then -ve as it moves back down to Earth. What is the 'something' ?

9. May 18, 2010

### Brittykitty

displacement? :\

10. May 18, 2010

### rock.freak667

no no, I am trying to get you to understand what the final velocity is at the maximum height.

Say you throw something up in the air. It does not continuously move upwards, eventually it fall back down, for it to change direction, what must it instantaneously do?

For a similar analogy, say you are driving forwards, for you to move backwards, what should happen to your forward velocity before you start to move backwards?

11. May 18, 2010

### Brittykitty

It would decrease velocity? =)

12. May 18, 2010

### rock.freak667

Right yes, as it moves up, it decrease velocity until it reaches what at the max height?

(Because for it to change direction, it needs to stop moving up and then start moving down)

13. May 18, 2010

### Brittykitty

final velocity?

14. May 18, 2010

### rock.freak667

If at the maximum height the object instantaneously stops, the final velocity is?

15. May 18, 2010

### Brittykitty

0? :)

16. May 18, 2010

### rock.freak667

Right! So v=0

v2=u2+2as

v=0
u2+2as = 0

(remember 'a' is negative)

17. May 18, 2010

### Brittykitty

Thanks! :)
So..
a=-9.81m/s
s=30.0m
v=0
u2??

How would I find the initial velocity now?

18. May 18, 2010

### Brittykitty

30*-9.81?

19. May 18, 2010

### rock.freak667

u2-2as=0

rearrange for u2 and then take the square root of both sides.