Question

CIE Further Math Mechanics question:
Two identical smooth balls, P and Q, are projected simultaneously towards each other from two points on horizontal ground. P is projected with speed u at an angle tan^-1(4/3) to the horizontal and Q is projected with speed ku at an angle tan^-1(3/40 to the horizontal ( diagram posted below). The balls collide when they are moving horizontally. It may be assumed that there is no air resistance. FInd the value of k.

Answer 1

The coefficient of restitution between the balls is e. Find, in terms of e, u and g, the distance between the points where the balls first hit the ground

Answer 2

@sarah786. Aha, I caught a helpful guy!

Answer 3

Sorry I'm not a math Student

Answer 4

Well, This is more physics than math, so probably you're not as incompetent as you think

Answer 5

I'm a Biology Student .Mostly help in biology and Chemistry .

Answer 6

Okay then, a bit disappointing though.

Answer 7

well you Should tag someone ales . There is nothin to disappoint btw

Answer 8

I mean nobody answers after an hour is quite disappointing, plus my friends all disappeared. That's really weird.

Answer 9

oh feel sad for you .. :(

Answer 10

may be the " @dumbcow " can help me

Answer 11

yep, it seems like the balls will meet at the apex of the parabola

you need to determine height function for each ball
apex is max height, max occurs when derivative equals 0

\[h(t) = -4.9t^{2} + v_o t\]
\[v_o = speed * \sin \theta\]

Answer 12

wait what does it mean "they collide when moving horizontally" ?

Answer 13

Yes, I think this is quite important

Answer 14

technically the only time they are only moving horizontally is at the apex, but each ball will have a different apex so that cant be when they collide ??

Answer 15

The answersays that we should equate vertical sped to zero

Answer 16

ok thats what i said

Answer 17

u*sina-gt=0=ku*sina, tana=4/3

Answer 18

sorry, should be ku*cosa-gt=0

Answer 19

but for Q, why is the vertical speed equal to ku*cosa

Answer 20

sin(b) = cos(a)

Answer 21

oh! yes!

Answer 22

OK, I got it!

Answer 23

But how about the second question?

Answer 24

hmm so k = tan(a)

Answer 25

yes, and tan(a) = 4/3

Answer 26

what is 2nd question

Answer 27

The coefficient of restitution between the balls is e. Find, in terms of e, u and g, the distance between the points where the balls first hit the ground

Answer 28

sorry i dont know what coefficient of restitution is?

set h(t) =0 to find when balls hit ground

Answer 29

e=separation/approach,

Answer 30

@Loser66

Answer 31

Do you have any idea?

Answer 32

That's very, very complicated......

Answer 33

I'm just confused about applying Newton's Law of Restitution to these kind of situations

Answer 34

@Loser66

Answer 35

the parametric equations are:
Ball P
\[x(t) = \frac{3}{5}t\]
\[y(t) = \frac{4}{5}t - \frac{g}{2} t^{2}\]

Ball Q:
\[x(t) = \frac{4}{3g} - \frac{16}{15}t\]
\[y(t) = \frac{4}{5}t - \frac{g}{2} t^{2}\]

here is graph of the parabolas formed by balls P,Q assuming u =1
P is blue line , Q is red line

the "x" distance between them initially is 4/(3g)

http://www.wolframalpha.com/input/?i=plot%28%284%2F3%29x+-+%2825g%2F18%29x%5E2%2C+%283%2F4%29%284%2F%283g%29+-x%29+-+%28225g%2F512%29%284%2F%283g%29+-x%29%5E2%29+for+x+%3D+0+to+4%2F%283*9.8%29+%2C+g+%3D+9.8