Since the carts stick together and come to rest after the collision, the initial speed of the 3.0-kg cart is 12 m/s.
Given the following data:
- Velocity of cart 1 = 9.0 m/s
To find the initial speed of the 3.0-kg cart, we would apply the law of conservation of momentum:
For a perfectly inelastic collision:
[tex]M_1V_1 - M_2V_2 = V_f(M_1 + M_2)[/tex]
When the carts stick together and come to rest after the collision, the final velocity is zero (0).
[tex]M_1V_1 - M_2V_2 = 0\\\\M_1V_1 = M_2V_2\\\\V_2 = \frac{M_1V_1}{M_2}[/tex]
Substituting the given parameters into the formula, we have;
[tex]V_2 = \frac{4(9)}{3}\\\\V_2 = \frac{36}{3}[/tex]
Initial speed = 12 m/s
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