A ball is thrown with a certain velocity (neglecting air resistance) and comes in contact with a wall, whilst in contact for 0.4s the ball bounces back'
And I have to work out the velocity at which the ball rebounds of the wall, the change in kinetic energy but I'm hoping you guys have come across these sort of questions before and that you'll be able to help me :P
I know you have to work out the horizontal and vertical components of the projection but I always get confused with some of the questions.
Hi, I'm doing further maths at A-level, and so I know what you need to know.
The question that you have given is incomplete like you said; you need to know the constant force that the wall is exerting on the ball, but never mind. It also involves impulses and forces, not just SUVAT.
You are right in saying you need to resolve the velocity/acceleration/forces in the two perpendicular directions (usually horizontal and vertical). The way to do this is to use the cosine/sine functions.
Then you write down all the information for the vertical motion, and then all the info for the horizontal motion.
The horizontal acceleration is always zero, and the downward acceleration is always 9.8m/s? (unless otherwise stated). You then choose the correct equation from the SUVAT equations (the one that only includes a value you don't know and you want to work out.)
e.g. "A Particle is projected at 30 degrees to the horizontal at v m/s, it lands 30m away at the same height that it was projected.
" find v
u = v
v = (we dont know, and dont care)
a = -9.8 (note the negative, because it is downwards)
s = 0 (because it has no vertical displacement)
t = t (we want to know this)
u = v
v = v
a = 0
s = 30
t = t (the same t that is in the verticle)
so for vertical, we choose the equation that doesn't have the final velocity in it, because we dont know it and we dont need to know it. this is:
S = ut + (1/2)*a*t?
Put the values in, rearrange for t.
We get: t = 0.1767v
then look at horizontal (replacing "t" with "0.1767v
We use any equation with S and t in it.
S = ut + (1/2)a*t?
30 = [v
= 28.8 m/s (I haven't checked through all this, so there m ight be a mistake, just wait for someone to confirm it)
For the Impulse/kinetic energy part of the question:
there are four formulas you might need for something like what you have asked:
F = ma
Impulse = force*time
Impulse = mv - mu
KE = (1/2)mv?
Here is a question you might get: A ball of 0.25kg hits a wall, and is travelling at 10 m/s. It is in contact with the wall for 0.4 seconds, and leaves the wall with a velocity of 5 m/s. What is the impulse exerted on the ball, and KE lost in the collision, and the constant force that was applied to the ball, from the wall.
(with the initial direction as positive)
Impulse = mv - mu
-Impulse = -(0.25*5) - +(0.25*10) [they all end up negative, and so they can all be changed to positive]
Impulse = 3.75 Ns (they almost always ask you about the unit "newton seconds" and you always get a mark for it, so get it right)
For the KE lost, just work out the KE before and then the KE after, and take the final one from the Intial one. NOTE: The direction of the ball doesn't matter, so the kinetic energy at one point should always end up positive.
For the constant force: just divide the impulse by the amount of time that the ball was touching the wall.
3.75/0.4 = 9.325 N.
Any questions? I probably just put much to much time into this answer, but never mind. If any of the calculations are wrong then tell me quickly.