In part \(a\) of Example 4.6, what are the directions of the changes in momentum, \(\Delta \vec{p}_{\mathrm{s}}\) and \(\Delta \vec{p}_{\mathrm{r}}\), of the two carts?

Data from Example 4.6

(a) A red cart with an initial speed of \(0.35 \mathrm{~m} / \mathrm{s}\) collides with a stationary standard cart \(\left(m_{\mathrm{s}}=1.0 \mathrm{~kg}\right)\). After the collision, the standard cart moves away at a speed of \(0.38 \mathrm{~m} / \mathrm{s}\). What is the momentum change for each cart? (b) The experiment is repeated with a blue cart, and now the final speed of the standard cart is \(0.31 \mathrm{~m} / \mathrm{s}\). What is the momentum change for each cart in this second collision? (c) If in the collisions \(v_{\mathrm{r} x, \mathrm{f}}=+0.032 \mathrm{~m} / \mathrm{s}\) and \(v_{\mathrm{b} x, \mathrm{f}}=-0.039 \mathrm{~m} / \mathrm{s}\), what are the inertias of the red and the blue carts?