A B C and E need help Thank you Let cl c2 and c3 be the conf

A, B, C, and E need help. Thank you!!

Let cl, c2, and c3 be the confidence values of the rules {p} - rightarrow{q}, {p} - rightarrow {q, r}, and {p, r} - rightarrow {q}, respectively. Which of the following relationships among c 1, c2, and c3 is IMPOSSIBLE? cl

Solution

mass of cart 1 is m = 0.5 kg

Initial velocity of cart 1 is u = 6.3 m/s

Initial velocity of cart 2 is M = 0

Final velocity of cart 1 is v = 0

Final velocity of cart 2 is V = 4.5 m/s

(a). Impulse delivered to cart 1 is J = m( v-u)

                                                  = 0.5 ( 0-6.3)

                                                  = - 3.15 kg m/s

Magnitude of impulse = 3.15 kgm/s

(b).Total momentum before collision = total momentum after collision

      mu + MU = mv +MV

   0.5(6.3) + 0 = 0.5(0) + M (4.5)

    3.15 = 4.5 M

From this mass of cart 2 is M = 3.15 / 4.5

                                            = 0.7 kg

(c). kinetic energy of cart 1 before collision K = (1/2)mu 2

                 K = 0.5 x 0.5 x 6.3 ²

                    = 9.9225 J

Kinetic energy of cart 2 after collision K \' = (1/2)MV ²

K \' = 0.5 x 0.7 x 4.5 ²

     = 7.0875 J

(e). Cart 3 collides with cart 2 and after collision they moves towards cart1 then they collides with cart1.