I need to solve for final velocities Va^2 and Vb^2. Equation 1 has two unknown v

Question

I need to solve for final velocities Va^2 and Vb^2.

Equation 1 has two unknown variables 15Va^2 + 8Vb^2 = 396 (Conservation of Momentum) The number2 in this equation are sub/not squared..I don't know how to type it correctly.

Equation 2 is 7.5 Va2^2 + 4 Vb2^2 = 3576 (Conservation of Energy)
Again, the first number 2 in each is sub (little 2), then it is squared.

I have to solve for either variable in Equation 1 then sub that into Equation 2 by doing it with a quadratic equation.

How do I do this?

Explanation / Answer

use the math equation editor to write the equations

equation 1   15Va2 + 8 Vb2 = 396

equation 2   7.5 Va22 + 4 Vb22 = 3576

solve equation 1 for Va2

15Va2 = 396 - 8 Vb2

Va2 = 26.4 - 0.533 Vb2

now substitute into equation 2

7.5 (26.4 - 0.533 Vb2)2 + 4 Vb22 = 3576

7.5(696.96 - 28.16 Vb2 + 0.2844 Vb22) + Vb22 = 3576

5227.2 - 211.2 Vb2 + 2.133 Vb22 + Vb22 = 3576

3.133 Vb22 - 211.2 Vb2 + 1651.2 = 0

solve this with the quadratic equation

Vb2 = (211.2 +/- sqrt(44605.44 - 4[(3.133)(1651.2)])/2(3.133)

Vb2 = (211.2 +/- 215.044)/6.266

Vb2 = 68.02 or Vb2 = - 0.613

you have to look at the problem and see which is physically correct

now just sub back into equation 1 to find Va2

Va2 = 26.4 - 0.533 Vb2

gives

Va2 = 22.77 or Va2 = 26.73

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