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M1 help please! heinemann exercise...

ok mechanics is like the WORST subject for me! i actually HATE it with a passion :frown:

ok this question seems so easy but i just can't do it! please help me out guys!

its exercise 3b in the edexcel heinemann book...

A stone is dropped from the top of a tower. one second later another stone is thrown vertically downwards from the same point with a velocity of 14ms-1. If they hit the ground together find the height of the tower.

so i was thinking, do i have to use simultaneous equations? i tried doing that with the second stone being (t+1) coz its thrown 1 sec later...i dont get the same answer as the back of the book though! how do i simultaneously solve this guys? or am i going about it the wrong way?

any help would be soo appreciated! thank you
Reply 1
Avatar for yazan_l
yazan_l
5
ok: (we will take down to be -ve)
for the first stone:
S = ut + ½at²
S = g/2 t²

for the second stone: it took it one second less to reach the ground... but it moved the same height... so:
S = u(t-1) + ½a(t-1)²
S = 14(t-1) + g/2 (t-1)²

so:
g/2 t² = 14(t-1) + g/2 (t-1)²
solve and find t, and then find S ( which is the height)
Reply 2
Avatar for rozzy
rozzy
OP
9
arghhhh thanks sooooo much! im so stupid! i got the two equations that you wrote but i didn't make them equal to each other....god i think im brain dead or something!

thankss! :smile:
rozzy

A stone is dropped from the top of a tower. one second later another stone is thrown vertically downwards from the same point with a velocity of 14ms-1. If they hit the ground together find the height of the tower.


For stone 1
s = h
t = t
u = 0
a = 9.8
v = ?

s = 0.5at^2 = 4.9t^2


For stone 2
s = h
t = t-1 (since it is in the air for 1 second less than stone 1)
u = 14
a = 9.8
v = ?

s = 14(t-1) + 0.5(9.8)(t-1)^2
=> s = 14(t-1) + 4.9(t-1)^2

At bottom of tower
4.9t^2 = 14t -14 + 4.9(t-1)^2
=> 4.9t^2 = 14t -14 + 4.9(t^2-2t+1)
=> 4.9t^2 = 14t - 14 + 4.9t^2 - 9.8t + 4.9
=> 0 = 14t - 14 - 9.8t + 4.9
=> 4.2t = 9.1
=> t = 9.1/4.2 = 2.17s

s = 4.9t^2 = 4.9(9.1/4.2)^2 = 23m
Reply 4
Avatar for rozzy
rozzy
OP
9
oh wait! lol i didnt get the same equations as you...i got (t+1) for the second stone...oh well close enough!

thanks again...you've cleared it up for me
rozzy
oh wait! lol i didnt get the same equations as you...i got (t+1) for the second stone...oh well close enough!

thanks again...you've cleared it up for me

Nah it's definitely t-1
t+1 gives you an answer that is way off.
Reply 6
Avatar for rozzy
rozzy
OP
9
ooh thanks too windowmaker :smile:
Reply 7
Avatar for rozzy
rozzy
OP
9
lol yeah i know...im so silly! its friday afternoon lol!
rozzy
ooh thanks too windowmaker :smile:

hehe, I love it when people call me that. :biggrin:

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