(a) Use Figure \(7.2 a\) to calculate the \(x\) components of the momenta of the two carts at \(t=30,60\), and \(90 \mathrm{~ms}\).

(b) What is the \(x\) component of the momentum of the system at each of these three instants?

Figure 7.2 Conservation of momentum and kinetic energy in an elastic collision between two carts on a low-friction track. The inertia of cart 1 is 0.12 kg, and that of cart 2 is 0.24 kg. before collision = 0 during collision cart 2 cart 1 cart 2 cart 1 (a) Velocity v, (m/s) 0.8 0.6 cart 2 0.4 0.2 interaction after collision X cart 2 cart 1 (b) Momentum P. (kg m/s) 0.16 cart 2 0.12 Speed of cart 1 changes twice as much 0.08 All as speed of cart 2. 0.04 Momentum of two-cart system is constant. interaction momentum of system cart 1 0 (ms) ) cart 1 30 40 50 60 70 80 90 30 40 50 60 70 80 it (ms) 90