The height of an object above the ground at time t is given by s=v0t - (g/2)t^2 where v0 is the initial velocity and g is the acceleration due to gravity.

a) At what height is the object initially?
s=__________
^^ i'm not quite sure how to find this... :(

b) How long is the object in the air before it hits the ground?
t=________
^^again, not very sure.. how would you set this equation up? :/

c) When will the object reach its maximum height?
t=_______

d) What is that maximum height?
t=_______

**not really sure how to set up this whole thing :( Please explain? THankss :)

Question

The height of an object above the ground at time t is given by s=v0t - (g/2)t^2 where v0 is the initial velocity and g is the acceleration due to gravity.

a) At what height is the object initially? 
s=__________
^^ i'm not quite sure how to find this... :(

b) How long is the object in the air before it hits the ground?
t=________
^^again, not very sure.. how would you set this equation up? :/

c) When will the object reach its maximum height?
t=_______

d) What is that maximum height?
t=_______

**not really sure how to set up this whole thing :( Please explain? THankss :)

agent0smith · Answer

s=v0t - (g/2)t^2

when t=0, what will s be? plug in t=0

anonymous · Answer

s=v0t-(g/2)0^2

s=v0t-0 ?

agent0smith · Answer

Plug in t=0 but do it better :P

anonymous · Answer

oh oops i forgot one! 

s=v0(0)-0= 0 ?

agent0smith · Answer

Good :)

 s=v0t - (g/2)t^2

Factor out the t...

 s=t( v0t - (g/2)t )

reaches the ground means s=0

 0=t( v0t - (g/2)t )

this would be far easier with equation editor too.

agent0smith · Answer

It's on the ground at t = 0 and...

v0t - (g/2)t = 0

try solving for t.

anonymous · Answer

t-(g/2)t=v0t ?

is that how to start it?

anonymous · Answer

this is part b right?

and part a was s=0 ? :)

agent0smith · Answer

yes ...oops my mistake

v0 - (g/2)t = 0 

-(g/2)t=v0

t = -2v0/g

anonymous · Answer

ohh okay haha :P

so that's as simplified as it can get right?

agent0smith · Answer

yeah. It's too hard to write that w/o equation editor, it'll do

c) When will the object reach its maximum height?
t=_______

It'll basically be the time above, divided by 2:

t = -2v0/g/2 = -v0/g

anonymous · Answer

yeah for some reason, the equation and draw tools still aren't working :(

agent0smith · Answer

oh my the last is the worst to do w/o the equation editor

d) What is that maximum height?
plug in the above t into
 s=v0t - (g/2)t^2

 s=v0(-v0/g) - (g/2)(-v0/g)^2

ew. You can simplify but i don't want to...

anonymous · Answer

hahaha okay..

so would it become
s=(-v0^2/g) - (g/2)(-v0^2/g^2) ?

 is that right? :/

and if so, would it simplify any more?

agent0smith · Answer

Wow, good job putting up with it! Yes :) but you can cancel off one of the g's in the second term there

agent0smith · Answer

s=(-v0^2/g) - (1/2)(-v0^2/g)

anonymous · Answer

ohhh okay awesome!! :) hehe thanks!!! :) the tools really need to start working again soon!!

agent0smith · Answer

Yes they really do :/