# Initial velocity

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?

rock.freak667
Homework Helper
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)

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

rock.freak667
Homework Helper
Hello :)
I'm not given the time so I'm assuming its v^2=u^2+2as ?

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

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 :\

rock.freak667
Homework Helper
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 :\

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'.

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'.

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

rock.freak667
Homework Helper
the final velocity would be (30.0m) (-9.81)?

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' ?

displacement? :\

rock.freak667
Homework Helper
displacement? :\

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?

It would decrease velocity? =)

rock.freak667
Homework Helper
It would decrease velocity? =)

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)

final velocity?

rock.freak667
Homework Helper
final velocity?

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

0? :)

rock.freak667
Homework Helper
0? :)

Right! So v=0

v2=u2+2as

v=0
u2+2as = 0

(remember 'a' is negative)

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

How would I find the initial velocity now?

30*-9.81?

rock.freak667
Homework Helper
Thanks! :)
So..
a=-9.81m/s
s=30.0m
v=0
u2??

How would I find the initial velocity now?

30*-9.81?

u2-2as=0

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