Answer :
To find the speed of the two cars together after the collision, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity. The direction of the momentum is taken into account as well.
Let's calculate the initial momentum of the red car:
- Momentum of red car = mass of red car * velocity of red car
- Momentum of red car = 972 kg * 57.0 m/s (to the east)
Next, let's calculate the initial momentum of the blue car:
- Momentum of blue car = mass of blue car * velocity of blue car
Since the blue car is traveling 18.0° south of west, we need to consider its velocity components in the horizontal and vertical directions. The horizontal component is 20.0 m/s * cos(18.0°) (to the east), and the vertical component is 20.0 m/s * sin(18.0°) (to the south).
Now, let's add the momentum components of the red and blue cars together to get the total momentum after the collision.
Total momentum after collision = momentum of red car + momentum of blue car
Finally, to find the speed of the two cars together, we divide the total momentum after the collision by the total mass of the system (the combined mass of the red and blue cars).
Speed of two cars together = total momentum after collision / total mass of the system
By calculating the appropriate values using the given information, we can determine the speed of the two cars together after the collision.
About velocity
Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It includes both magnitude (speed) and direction. The magnitude of velocity is the speed at which an object is moving, while the direction of velocity indicates the object's movement along a specific path or in a particular direction.
Velocity is calculated by dividing the change in position (displacement) of an object by the time taken for that displacement. Mathematically, it can be expressed as:
Velocity (v) = Displacement (Δx) / Time (Δt)
The units of velocity are typically expressed in meters per second (m/s) in the International System of Units (SI), but other units such as kilometers per hour (km/h) or miles per hour (mph) can also be used depending on the context.
It's important to note that velocity is different from speed, as velocity takes into account both the magnitude and direction of motion, while speed only refers to the magnitude.
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