Question

1. in a collision, a 15 kg object moving with a velocity of 3 m/s transfers all of its momentum to a 5 kg object. what would be the velocity of the 5 kg object after the collision? (hint: think about the law of conservation of momentum and draw a picture of what is happening to get started!)

Explanation:

Step1: Find the initial momentum of the 15 - kg object

The formula for momentum is \(p = mv\). For the 15 - kg object with \(m = 15\space kg\) and \(v=3\space m/s\), the initial momentum \(p_{15}=15\times3\).

$$p_{15}=45\space kg\cdot m/s$$

Step2: Apply the law of conservation of momentum

According to the law of conservation of momentum \(p_{initial}=p_{final}\). Before the collision, only the 15 - kg object has momentum. After the collision, all of its momentum is transferred to the 5 - kg object. Let the velocity of the 5 - kg object be \(v_{5}\). Using \(p = mv\) again, with \(p = 45\space kg\cdot m/s\) and \(m = 5\space kg\), we have \(45=5\times v_{5}\). Solving for \(v_{5}\), we get \(v_{5}=\frac{45}{5}\).

$$v_{5} = 9\space m/s$$

Answer:

The velocity of the 5 - kg object after the collision is \(9\space m/s\).