Find Initial Velocity Formula | 30.0m Height

[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 don't quite remember how to do this. Is it 30.0m / 9.81[m/s]^2?

 

[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)

 

[Brittykitty]

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

 

[rock.freak667]

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.

 

[Brittykitty]

Thank you! :)
one more question, how would I find the initial velocity? Would it be 0? or 9.81[m/s]^2? don't remember that part either :\

 

[rock.freak667]

Thank you! :)
one more question, how would I find the initial velocity? Would it be 0? or 9.81[m/s]^2? don't 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'.

 

[Brittykitty]

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]

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' ?

 

[Brittykitty]

displacement? :\

 

[rock.freak667]

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?

 

[Brittykitty]

It would decrease velocity? =)

 

[rock.freak667]

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)

 

[Brittykitty]

final velocity?

 

[rock.freak667]

final velocity?

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

 

[Brittykitty]

0? :)

 

[rock.freak667]

0? :)

Right! So v=0

v²=u²+2as

v=0
u²+2as = 0


(remember 'a' is negative)

 

[Brittykitty]

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

How would I find the initial velocity now?

 

[Brittykitty]

30*-9.81?

 

[rock.freak667]

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.