for #9 its elastic question so i understand i have to use COM, COKE.. but like i

Question

for #9 its elastic question so i understand i have to use COM, COKE..

but like in the paper, COM: 5vif+15v2f=5(-7)+15(3)=10...

so  5vif+15v2f=10 -> v1f + 3 v2f.. why the hell he divide this by 5? to eliminate ??? do you always have to do that?

also, for COKE part: v1f - v2f= -(-7-3)=10.. ok now its messing me up. because i learned that formula for COKE is (v1i-v2i)=-(v1f-v2f) not like v1f - v2f= -(-v1i-v2i)=10..???  what he did it above is reversed.... is that mistake he did?

anyways, so it seems like he did [ v1f + 3 v2f =2 ] + (mulitply by -1)* [ v1f - v2f= -(-7-3)=10 ]

why the heck he multiply by -1 to get ride of v1f i know..!! but then whole thing should be multiply by -1 right?

...so damn confused..help

In the hanging steel balls apparatus, when one ball at one end is dropped, why does one ball at the other end pop out at the same speed instead of two balls with half the speed, which would satisfy COM? A hooking mechanism on an aircraft carrier's deck can arrest a landing 6,000-Kg jetfighter with a force configuration as shown in the graph below. Determine the plane's maximum allowable touch-down speed. A 5Kg golf ball moving at -7m/s collides elastically head-on with a 15Kg bowling ball moving at +3 m/s. Find the vf of each ball after the collision. A moving train wagon collided with a smaller stationary one. The two wagons got tangled together and moved along the track at 6m/s after the collision. If the mass of the small wagon is one third that of the bigger wagon, what's the initial speed of the big wagon?

Explanation / Answer

for #10 solution is clearly written
by using moment conservation mv1+m'v'1=mv2+m'v'2
m' = m/3
v2=v'2 = 6m/s ; v'1= 0 m/s (statinary wagon)
so mv1 +0 = (m+m/3 )(6)
mv1 = 4m/3 * 6
mv1 = 8m
v1 = 8m/s

for #9
its elastic question soyou have to use COM, COKE..
COM
5vif+15v2f=10
v1f + 3 v2f =2
he divied by 5 to simplfy equation ,you don't have to divide every time online when you think that this will help then u can divide or multiply equation by any constant
for coke part
(v1i-v2i)=-(v1f-v2f) this is formula u know
if x=-y then y =-x also true
same thing he did (v1f-v2f) =-(v1i-v2i)
so he didn't make any mistake

so it seems like he did [ v1f + 3 v2f =2 ] + (mulitply by -1)* [ v1f - v2f= -(-7-3)=10 ]

he multiply bcos he can eliminate v1f
he has to eliminate one unknown to solve these equns so he did
:)

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