Question

Two cars, each of mass \(1300 \mathrm{kg},\) are approaching each other on a head-on collision course. Each speedometer reads $19 \mathrm{m} / \mathrm{s} .$ What is the magnitude of the total momentum of the system?

Short answer

Solution: Step 1: Analyze the given information The mass of each car is 1300 kg, and their speeds are 19 m/s. Step 2: Calculate momentum momentum_car1 = 1300 kg × 19 m/s = 24,700 kg·m/s momentum_car2 = 1300 kg × (-19 m/s) = -24,700 kg·m/s Step 3: Find the total momentum total_momentum = momentum_car1 + momentum_car2 = 24,700 kg·m/s + (-24,700 kg·m/s) = 0 kg·m/s Step 4: Calculate the magnitude of the total momentum magnitude_total_momentum = abs(0) = 0 kg·m/s The magnitude of the total momentum of the system is 0 kg·m/s.

Step-by-step solution

Analyze the given information

We are given the mass of each car (1300 kg) and their speeds (19 m/s). As they are approaching each other in a head-on collision, we know their velocities have opposite directions.

Calculate momentum

Momentum is given by the formula: momentum = mass × velocity. For each car, we can now calculate the momentum: momentum_car1 = 1300 kg × 19 m/s momentum_car2 = 1300 kg × (-19 m/s) (since it's in the opposite direction)

Find the total momentum

Now we will add the momenta of the two cars to find the total momentum of the system: total_momentum = momentum_car1 + momentum_car2

Calculate the magnitude of the total momentum

Finally, we will calculate the magnitude of the total momentum, which is simply the absolute value of the total momentum: magnitude_total_momentum = abs(total_momentum) Now, let's perform the calculations.