You place a \(0.10-\mathrm{kg}\) sonic ranger on a low-friction track in front of a \(0.50-\mathrm{kg}\) cart to measure the cart's velocity in the Earth reference frame, which turns out to be \(+(1.0 \mathrm{~m} / \mathrm{s}) \hat{\imath}\). You are distracted, the cart hits the ranger in a totally inelastic collision, and the two objects then move forward together. A friend is running toward the cart with a velocity of \(-(3.0 \mathrm{~m} / \mathrm{s}) \hat{t}\) with her sonic ranger on and pointed at the cart.

(a) What is the momentum of the cart, with the ranger stuck to it, in your friend's reference frame?

(b) What velocity does her sonic ranger measure for the cart after the collision?