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Anyway,

I have 3 questions, all of which I have done the work for, but don't know if it's correct, take a look and give some feedback. Thanks.

1)A mine car, whosse mass is 440kg, rolls at a speed of 0.50m/s on a horizontal track. A 150kg chunk of coal has a speed of 0.80 m/s when it leaves the chute at an angle of 25 degrees with respect to the horizontal. Determine the velocity of the car/coal system after the coal has come to rest in the car.

Ok, so

mV (coal)+ mV (cart) = [m(coal)+m(cart)]Vtotal

150kg (Vcos 25.0) +440kg (0.50m/s)= (150kg+440kg) x Vtotal

Vtotal = (328.75kgm/s)/590 kg

Vtotal= 0.557m/s.

Well it sort of makes sense as the speed would slow down if the extra weight is added, but I left the Y component out of this...

2) Two identical balls are travelling towrd each other with velocities of -4.0 and +7.0 m/s and they experience an elastic head on collision. Obtain the velocities of each ball after the collision.

ok seems easy enough.

mV(ball 1) + mV (ball 2) = mV (ball1 after)+ mV (ball 2 after)

punch in all the numbers I get: V(ball1after)= +3.0m/s-V(ball2 after)

2 variables I don't know, try to get a sys of equation. Ke initial = Ke final because it's elastic.

1/2mv^2(ball1initial)+1/2mv^2(ball 2 intial) = 1/2mv^2+1/2mv^2

ok all the 1/2's and the respective masses cancel? right...

so I'm left with after I punch in the numbers: (7.0m/s)^2 +(-4.0m/s)^2 =

V^2(ball 1 final)+ V^2 (ball2 final)

OR 65m/s = V^2(ball 1 final)+V^2 (ball 2 final)

So I get two equations: 3.0m/s-V(ball2 final)= V(ball 1 final) <==I square everything so I can substitute in 65m/s = V^2(ball 1 final)+V^2 (ball 2 final)

After squaring and substituting I get a quadratic equation of this form:

2V^2 (ball 2 final) - 2V (b2 final) -56 m/s

I then use the x= [-b +/- (4ac)^1/2]/2a to get my V (ball2 final).

MY QUESTION is since we square root the 4ac, my c value is negative, and my "a" is positive, so a square root of a negative value?? does that work?

But anyway I get 6.79 m/s for ball 2 final and after sub back into previous equations I get V ball 1 final to be -3.791 m/s. The directions make sense since it'll rebound, but the magnitude...any ideas?

Thanks all.