Question

Assume: Moving to the right is positive. A(n) 10 g object moving to the right at 29 cm/s makes an elastic head-on collision with a 14 g object moving in the opposite direction at 42 cm/s. 10 g 29 cm/s 14 g 42 cm/s Find the velocity of the first object immediately after the collision. Answer in units of cm/s

Answer 1

Assuming the momenum is conserved,

m₁v_1i + m₂v_2i = m₁v_1f + m₂v_2f

From relative velocity, we have

v_1i - v_2i = v_2f - v_1f

v_2f = v_1i - v_2i + v_if

Put this in momnetum equation and simplify , we get

m₁v_1i + m₂v_2i - m₂ (v_1i - v_2i) = v_1f (m₁ + m₂)

v_1f = m₁v_1i + m₂v_2i - m₂ (v_1i - v_2i) / (m₁ + m₂)

Now,, just put all the values, Remember to put the sign also,

v_1f = 10*29 - 14*42 - 14(29 - (-42) / 14 + 10

v_1f = -298 - 994 / 24

v_1f = - 53. 8333 m/s

or we can say, object 1 has 53.8333 m/s in negative direction ( to the left)