Question

name:
1> calculate the momentum of a 1200kg car with a velocity of 25m/s.

1. what is the momentum of a child and wagon if the total mass of the child and wagon is 22kg and the velocity is 1.5m/s?
2. the parking brake on a 1200kg automobile has broken, and the vehicle has reached a momentum of 7800kg.m/s. what is the velocity of the vehicle?
3. a toy dart gun generates a dart with 140kg.m/s momentum and a velocity of 4m/s. what is the mass of the dart in grams? (hint: figure kg, then convert answer to grams)
4. a bowling ball of 35.2kg, generates 218 kg.m/s units of momentum. what is the velocity of the bowling ball?
5. a school bus traveling at 40 km/hr. (11.1m/s) has a momentum of 152625 kg.m/s. what is the mass of the bus?

Explanation:

Step1: Recall the formula for momentum

Momentum \( p = mv\), where \(m\) is mass and \(v\) is velocity.

Step2: Substitute values for problem 1

Given \(m = 1200\space kg\) and \(v=25\space m/s\), then \(p=(1200)(25)\).

$$p = 30000\space kg\cdot m/s$$

Step3: Substitute values for problem 2

Given \(m = 22\space kg\) and \(v = 1.5\space m/s\), then \(p=(22)(1.5)\).

$$p=33\space kg\cdot m/s$$

Step4: Rearrange formula for problem 3

From \(p = mv\), we get \(v=\frac{p}{m}\). Given \(p = 7800\space kg\cdot m/s\) and \(m = 1200\space kg\), then \(v=\frac{7800}{1200}\).

$$v = 6.5\space m/s$$

Step5: Rearrange formula for problem 4

From \(p = mv\), we get \(m=\frac{p}{v}\). Given \(p = 140\space kg\cdot m/s\) and \(v = 4\space m/s\), then \(m=\frac{140}{4}=35\space kg\). Convert to grams: \(35\times1000 = 35000\space g\).

Step6: Rearrange formula for problem 5

From \(p = mv\), we get \(v=\frac{p}{m}\). Given \(p = 218\space kg\cdot m/s\) and \(m = 35.2\space kg\), then \(v=\frac{218}{35.2}\approx6.19\space m/s\).

Step7: Rearrange formula for problem 6

From \(p = mv\), we get \(m=\frac{p}{v}\). Given \(p = 152625\space kg\cdot m/s\) and \(v = 11.1\space m/s\), then \(m=\frac{152625}{11.1}=13750\space kg\).

Answer:

1. \(30000\space kg\cdot m/s\)
2. \(33\space kg\cdot m/s\)
3. \(6.5\space m/s\)
4. \(35000\space g\)
5. \(\approx6.19\space m/s\)
6. \(13750\space kg\)