A ball of mass m 1 = 43.9 g moving at aconstant speed of 22.28 m/s collides head

Question

A ball of massm1 = 43.9 g moving at aconstant speed of 22.28 m/s collides head-on with astationary ball of mass m2 =316.5 g. The collision is elastic. What is the velocity ofthe first ball immediately after the collision?
I solved the equation for elastic collisions. Then I used thev1 -v2=(-v1-v2) and solved v2 in terms of v1. I plugged it backinto the first equation and got -18.21 m/s. But that is incorrect.What I am doing incorrect? A ball of massm1 = 43.9 g moving at aconstant speed of 22.28 m/s collides head-on with astationary ball of mass m2 =316.5 g. The collision is elastic. What is the velocity ofthe first ball immediately after the collision?
I solved the equation for elastic collisions. Then I used thev1 -v2=(-v1-v2) and solved v2 in terms of v1. I plugged it backinto the first equation and got -18.21 m/s. But that is incorrect.What I am doing incorrect?

Explanation / Answer

Given that the masses are m1 = 43.9 g = 0.0439kg and m2 = 0.3165 kg Initial velocities are u1 = 22.28 m/s and u2 = 0m/s --------------------------------------------------------- Let the masses of the two bodies are m1 and m2
        the initial velocitiesare U1,U2 respectively
       the final velocitiesare V1,V2 respectively. from the law of conservation of momentum             m1*U1+m2*U2 = m1*V1+m2*V2                       m1(U1-V1) = m2*(V2 - U2)    ----------(1)   from the law of conservation of Kineticenergy             (1/2)m1*U12+(1/2)m2*U22 =(1/2)m1*V12+ (1/2)m2*V22            m1(U12-V12) = m2*(V22 -U22 )   ----------(2) devide the equation (1) by (2) weget                      U1+V1 = V2 +U2              V1 =V2 + U2  -U1              V2   = U1+V1 -U2             substitude the valueof   V2 value in equation (1) weget                         V1 = (m1-m2)*U1/(m1+m2) + (2m2)U2 /(m1+m2)-----------(3)          substitudethe value of   V1 value in equation (1) weget                      V2 = (m2-m1)U2 /(m1+m2) + (2m1)U1 /(m1+m2)                  -----------(4) ------------------------------------------------------------------------------------------------------------- From the equation (3) we get final velocity fo the massm1 after collision is                     V1 = (m1-m2)*U1/(m1+m2) + 0                           = (m1-m2)*U1/(m1+m2)                           = ------------ m/s            m1(U12-V12) = m2*(V22 -U22 )   ----------(2) devide the equation (1) by (2) weget                      U1+V1 = V2 +U2              V1 =V2 + U2  -U1              V2   = U1+V1 -U2             substitude the valueof   V2 value in equation (1) weget                         V1 = (m1-m2)*U1/(m1+m2) + (2m2)U2 /(m1+m2)-----------(3)          substitudethe value of   V1 value in equation (1) weget                      V2 = (m2-m1)U2 /(m1+m2) + (2m1)U1 /(m1+m2)                  -----------(4) ------------------------------------------------------------------------------------------------------------- From the equation (3) we get final velocity fo the massm1 after collision is                     V1 = (m1-m2)*U1/(m1+m2) + 0                           = (m1-m2)*U1/(m1+m2)                           = ------------ m/s     V1 =V2 + U2  -U1              V2   = U1+V1 -U2             substitude the valueof   V2 value in equation (1) weget                         V1 = (m1-m2)*U1/(m1+m2) + (2m2)U2 /(m1+m2)-----------(3)          substitudethe value of   V1 value in equation (1) weget                      V2 = (m2-m1)U2 /(m1+m2) + (2m1)U1 /(m1+m2)                  -----------(4) ------------------------------------------------------------------------------------------------------------- From the equation (3) we get final velocity fo the massm1 after collision is                     V1 = (m1-m2)*U1/(m1+m2) + 0                           = (m1-m2)*U1/(m1+m2)                           = ------------ m/s         V2   = U1+V1 -U2             substitude the valueof   V2 value in equation (1) weget                         V1 = (m1-m2)*U1/(m1+m2) + (2m2)U2 /(m1+m2)-----------(3)          substitudethe value of   V1 value in equation (1) weget                      V2 = (m2-m1)U2 /(m1+m2) + (2m1)U1 /(m1+m2)                  -----------(4) ------------------------------------------------------------------------------------------------------------- From the equation (3) we get final velocity fo the massm1 after collision is                     V1 = (m1-m2)*U1/(m1+m2) + 0                           = (m1-m2)*U1/(m1+m2)                           = ------------ m/s     substitude the valueof   V2 value in equation (1) weget                         V1 = (m1-m2)*U1/(m1+m2) + (2m2)U2 /(m1+m2)-----------(3)          substitudethe value of   V1 value in equation (1) weget                      V2 = (m2-m1)U2 /(m1+m2) + (2m1)U1 /(m1+m2)                  -----------(4) ------------------------------------------------------------------------------------------------------------- From the equation (3) we get final velocity fo the massm1 after collision is                     V1 = (m1-m2)*U1/(m1+m2) + 0                           = (m1-m2)*U1/(m1+m2)                           = ------------ m/s

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