Forthe following question ***only*** these three physics formulas can beused since this is intended to help us practice our algebra skills:

X: m1v1o +m2v2o=m1v1fcos θ1+m2v2f cosθ2

Y:0=M1V1fsinθ1+M2V2fSinθ2

KE= 1/2m1v^2(1 initial) + 1/2m(2)v^2(2 initial) = 1/2m1v^2(1 final) + 1/2m2v^2(2 final)

Thisformula CANNOTBE USED: (M1V1+M2V2)/(M1+M2)I know how to figure it out with this formula but unfortunately Ican'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°

Thisis what I have so far:

X:m1v1o +m2v2o=m1v1fcos θ+m2v2f cosθ

(20Kg)(30 m/s) + (8kg) (0 m/s) =(20kg) v1fcos θ+(8kg)v2f cos40°

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

Ithen did x^2 + Y^2

(600-6.12836V2F)^2+(20V1Fcosθ^)2

(-5.1423V2F)^2=(20V1fsinθf)^2

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

whichthen becomes

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

Y:26.443V2F=400(V1fsin θ)^2

Whichadded together is:

360,000-7354.032V2F+63.99V2F^2=800(V1Fcosθ)^2+(V1fsin θ)^2

cos+sinequals 1 so

360,000-7354.032V2F+63.99V2F^2=800V1F

Andthen used the quadratic formula

a=63.995b=7354.03 c= 360,000

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

butthe square root is negative…so i can't continue???

I'massuming 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 hereto get V2f??? KE= 1/2m1v^2(1 initial) + 1/2m(2)v^2(2 initial) = 1/2m1v^2(1 final) + 1/2m(2)v^2(2 final)

andthen 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.