Colliding Objects done the hard way

For the following question ***only*** these three physics formulas can be used since this is intended to help us practice our algebra skills:

X: m1v1o +m2v2o =m1v1fcos θ1+m2v2f cos θ2

Y: 0=M1V1fsinθ1+M2V2fSinθ2

KE= 1/2m1 v^2(1 initial) + 1/2m(2)v^2(2 initial) = 1/2m1 v^2(1 final) + 1/2m2v^2(2 final)

This formula CANNOT BE USED: (M1V1+M2V2)/(M1+M2) I know how to figure it out with this formula but unfortunately I can’t use it

Question: two objects collide, find V2F and V1F and θ1F. The given values are

M1= 20 kg; V1 initial = 30 m/s M2=8kg V2 initial = 0 m/s θ2= 40°

This is what I have so far:

X: m1v1o +m2v2o =m1v1fcos θ+m2v2f cos θ

(20 Kg)(30 m/s) + (8kg) (0 m/s) =(20kg) v1f cos θ+ (8kg)v2f cos 40°

600+0 = (20kg) v1fcos θ+ 6.128vf2

600 – 6.128v2f= (20kg) v1f cos θ

Y: 0 = M1V1F sin θ ° + M2V2F sin θ

0 = (20kg) (ViF)sin θ+(8kg)(V2F) sin 40 °

0 =(20kg) (ViF)sin θ +5.142V2F

-5.142V2F= (20kg) (ViF)sin θ

I then did x^2 + Y^2

(600-6.12836V2F)^2+(20V1Fcos θ^)2

(-5.1423V2F)^2=(20V1fsin θf)^2

X: 360,000-3677.016V2F-3677.016V2F+37.552V2F^2=400(V1fcos θ)^2

which then becomes

X: 360,000-7354.032V2F-+37.552V2F^2=400(V1fcos θ)^2

Y: 26.443V2F=400(V1fsin θ)^2

Which added together is:

360,000-7354.032V2F+63.99V2F^2=800(V1Fcos θ)^2+(V1fsin θ)^2

cos+sin equals 1 so


And then used the quadratic formula

a=63.995 b=7354.03 c= 360,000

+7354.03+- (square root -7354.03^2(63.995)(360,000))/ 2(63.995) = 800V1F

but the square root is negative…so i can’t continue???

I’m assuming once I figure out whats wrong with the quadratic formula, one of the answers would be useable so it’d be answer=800V1F and then solve to figure out what the answer is???? and then I’d plug into here to get V2f??? KE= 1/2m1 v^2(1 initial) + 1/2m(2)v^2(2 initial) = 1/2m1 v^2(1 final) + 1/2m(2)v^2(2 final)

and then for angle = -tan (V1f/V2f)

I was told by an online tutor that “Actually you have done correct till finding v1fsinO after that simply divide v1fcosO to find tan and angle then use that to find any other value as v1f and v1f will cancel out during division.” BUT this makes no sense to me since i’m STILL STUCK on the quadratic equation bit

Please let me see how you manage to solve this problem, i’ve been trying to do it any spare moment i’d had for this last week but I’m having no luck.

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