The final velocity of the red cart is 1.67 m/s to the right
Explanation:
We can solve the problem by using the law of conservation of momentum: in fact, in absence of external forces, the total momentum of the two carts before and after the collision must be conserved.
So we can write:
[tex]p_i = p_f\\m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2[/tex]
where:
[tex]m_1 = 0.26 kg[/tex] is the mass of the blue cart
[tex]u_1 = 30.8 m/s[/tex] is the initial velocity of the blue cart (we take the right as positive direction)
[tex]v_1 = 0[/tex] is the final velocity of the blue cart
[tex]m_2 = 4.8 kg[/tex] is the mass of the red cart
[tex]u_2 = 0[/tex] is the initial velocity of the red cart
[tex]v_2[/tex] is the final velocity of the red cart
Re-arranging the equation and substituting the values, we can calculate the final velocity of the red cart:
[tex]v_2 = \frac{m_1 u_1}{m_2}=\frac{(0.26)(30.8)}{4.8}=1.67 m/s[/tex]
And since the sign is positive, the direction is the same as the initial direction of the blue cart (so, to the right).
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