Mechanics

dmg24

Old buddies, old chaps,

Can I ask for some Mechanics help please? I have had a go at this question, but really have no idea if I am on the right tracks, and feel too silly to publish my answers!

So here is the question:

A ball is dropped from a height of 18m. As it falls, its speed at time t seconds is given by v = 9.8t ms^-1.

(a) Sketch a graph of speed against time and find the acceleration (I figure this is a straight line graph originating at 0,0, with points at 1,9.8 and 2,19.6?).

(b) Find a formula for the distance travelled by the ball in t seconds.

(c) How long does it take for the ball to reach the ground?

My answer to (b) seems a bit random, and hence my answer to (c) could well be wrong too.

Thanks in advance ... think I might cry if my answer is wrong! x

melancholly

right - it's been almost 9 years since i did mechanics, so can you remind the thicko here of all hte nice standard equations (speed = distance/time, force = mass x acceleration is all i get after 5 mins of thinking... i know there's a u^2 and v^2 one that seems reasonably relevant!)

dmg24

We've got ...

v = u + at

s = ut + (1/2)at^2

v^2 = u^2 + 2as

s = (1/2) (u + v) t

Thanks! x

melancholly

ok - take with huge pinch of salt as likely to be wrong:

(b) s=4.9t^2
(c) when s=18, t=1.9ish seconds?

that was a mental workout for me.....! hope it's close to what you got!

dmg24

It isn't, but you are much more likely to be right than me!

I can see why our answers differ though ...

For b, I used s = ut + 1/2at^2

I assumed that u would be 9.8t^2 and t = 1, but is the initial speed actually 0? That would make sense to me, but then would I always assume an initial speed of 0, unless I am told otherwise?

Believe it or not I could be teaching this in a matter of months!

melancholly

ok - i used s=1/2(u + v)t and assumed that u was zero... i guess when the used hte term 'dropped' it had to be at zero to start with?!

atually yes - u must be 0, or v wouldn't be 9.8t (going with the v=u+at one)

dmg24

Fantastic - you have taught me more in half an hour than my lecturer did in a term.

I think I might go and lie down now, can't do anymore work as the cat is lying on my file, and he is just too cute to move him!

Thank you so much! x

melancholly

lolol glad i could help!
have been avoiding work all day so this counts as something productive instead!!