Question

a cannon sits on a stationary railroad flatcar with a total mass of 1000 kg. when a 10 - kg cannon ball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar? a. 0 m/s b. 0.5 m/s to the right c. 1.0 m/s to the right d. 20 m/s to the right e. 50 m/s to the right

Explanation:

Step1: Apply the law of conservation of momentum

The initial momentum of the system (cannon + flatcar + cannon - ball) is \(P_{i}=0\) (since it is stationary). According to the law of conservation of momentum \(P_{i} = P_{f}\), where \(P_{f}=m_{1}v_{1}+m_{2}v_{2}\). Let \(m_{1} = 10\space kg\), \(v_{1}=- 50\space m/s\) (left - direction), \(m_{2}=1000\space kg\), and \(v_{2}\) be the velocity of the flatcar.

Step2: Solve for \(v_{2}\)

$$
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The positive sign indicates the direction is to the right.

Answer:

B. \(0.5\space m/s\) to the right