Question

(a) what is the momentum in kg · m/s of a garbage truck that is 1.40 × 10⁴ kg and is moving at 28.0 m/s?
kg · m/s
(b) at what speed in m/s would an 8.00 kg trash can have the same momentum as the truck?
m/s

Explanation:

Step1: Calculate the momentum of the garbage truck

The formula for momentum is \(p = mv\). Given \(m = 1.40\times10^{4}\text{ kg}\) and \(v = 28.0\text{ m/s}\), we substitute these values into the formula:
\(p=(1.40\times 10^{4})\times28.0\)
\(p = 1.40\times28.0\times10^{4}\)
\(p=39.2\times10^{4}\)
\(p = 3.92\times 10^{5}\text{ kg}\cdot\text{m/s}\)

Step2: Calculate the speed of the trash - can

Since the momentum of the trash - can \(p = mv\) and \(p\) (trash - can) \(=p\) (truck) \(=3.92\times 10^{5}\text{ kg}\cdot\text{m/s}\), and \(m = 8.00\text{ kg}\).
We solve for \(v\) using the formula \(v=\frac{p}{m}\)
\(v=\frac{3.92\times 10^{5}}{8.00}\)
\(v = 4.9\times10^{4}\text{ m/s}\)

Answer:

(a) \(3.92\times 10^{5}\)
(b) \(4.9\times 10^{4}\)