The Principle of Conservation of Momentum

How can we calculate the velocity of the dart right before it hits the car using the principle of conservation of momentum?

Given the distance traveled is 1.65m, time taken is 1.40s, average speed during coast is 1.178 m/s, speed of the dart/car immediately after impact is 2.356m/s, mass of the dart is 0.0057 kg, and mass of the car is 0.045 kg.

Calculating the Velocity of the Dart

To find the velocity of the dart right before it hits the car, we can utilize the principle of conservation of momentum. This principle states that the total momentum before a collision is equal to the total momentum after the collision.

When a dart is shot and hits a toy car, we can use the conservation of momentum to determine the velocity of the dart right before impact. The momentum of an object is calculated by multiplying its mass by its velocity. In this case, we have the mass of the dart and the mass of the car, along with the velocities before and after impact.

First, we need to calculate the initial velocity of the dart before it hits the car. We can set up an equation where the momentum of the dart before impact is equal to the momentum of the dart-car system after impact. This equation involves the masses and velocities of both the dart and the car.

Here is the formula we can use to calculate the velocity of the dart right before it hits the car:

By plugging in the given values and solving for the initial velocity of the dart, we can determine the velocity of the dart right before impact. This calculation allows us to understand the motion and interactions between the dart and the car in this scenario.

By applying the principle of conservation of momentum, we can analyze the dynamics of the dart-car collision and determine the velocity of the dart at the crucial moment before impact.