Question

a blue lab cart is traveling west on a track when it collides with and sticks to a red lab cart traveling east. the magnitude of the momentum of the blue cart before the collision is 2.0 kilogram · meters per second, and the magnitude of the momentum of the red cart before the collision is 3.0 kilogram · meters per second. the magnitude of the total momentum of the two carts after the collision is
a 1.0 kg·m/s
b 2.0 kg·m/s
c 3.0 kg·m/s
d 5.0 kg·m/s

Explanation:

Step1: Define direction signs

Let east be positive, west be negative.

Step2: Assign momentum values

Blue cart momentum: $p_b = -2.0\ \text{kg·m/s}$
Red cart momentum: $p_r = 3.0\ \text{kg·m/s}$

Step3: Apply conservation of momentum

Total final momentum = total initial momentum:
$p_{total} = p_b + p_r$
$p_{total} = -2.0 + 3.0$

Step4: Calculate magnitude

$|p_{total}| = |1.0| = 1.0\ \text{kg·m/s}$

Answer:

A. 1.0 kg·m/s