Respuesta :
By using conservation of momentum and conservation of energy we can calculate that the initial speed of the 2.0 kg object is 12.25 m/s.
According to the conservation of momentum, the total momentum before elastic collision will be equal to the total momentum after the collision. Here we need to note that collision should be elastic it means there is no loss of energy in any form has occurred. so we can write that
before collision (m1v1bf + m2v2bf) = after collision(m1v1af+m2v2af)
Here m1 and v1bf are the mass and velocity of the one object and m2 and v2bf are the mass and velocity of the another object. Here v1bf, v2bf are the velocities before collision and v1af and v2af are the velocities after collision.
putting the appropriate values, we get
2v1bf + 5x 0 = 2 x v1af + 5 x 7
2v1bf = 2v1af + 35
v1bf = v1af + 17.5
again, since the collision is elastic so energy transferred would have reduced the velocity of m1
it means
[tex]\frac{m1 (v1bf^{2} - v1af^{2} )} {2}= \frac{m2v2^{2} }{2}[/tex]
putting the values, we get
2(v1bf^2 -v1af^2) = 5 x 49
(v1bf - v1af) (v1bf + v1af) = 2.5 x 49
(v1bf + v1af) = 7
since v1bf - v1af = 17.5
2v1bf = 24.5
v1bf = 24.5/2
v1bf = 12.25 m/s
Hence the initial speed before collision of the 2.0 kg object is 12.25 m/s .
To learn more about conservation of momentum, visit here
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