Final answer:
The x-component of momentum for an 890-kg car moving at 22 m/s at an angle of 210 degrees with respect to the x-axis is -9768.6 kg·m/s.
Step-by-step explanation:
The question asks to find the x-component of momentum of a car that has a mass of 890 kg and is moving at a speed of 22 m/s at an angle of 210 degrees relative to the x-axis. Momentum is a vector quantity defined as the product of an object's mass and its velocity. To find the x-component of the car's momentum, we can use the formula:
px = p × cos(θ)
Where px is the x-component of momentum, p is the magnitude of the total momentum (mass × velocity), and θ is the angle made with the positive x-axis. In this scenario, we need to be mindful of the angle's direction and use trigonometric functions correctly.
Momentum, p = mass × velocity
Momentum, p = 890 kg × 22 m/s
Momentum, p = 19580 kg·m/s
At an angle of 210 degrees, the x-component would be:
px = p × cos(210°)
px = 19580 × cos(210°)
Since cos(210°) is negative, the x-component of momentum will also be negative, signifying that it is in the opposite direction of the positive x-axis.
Calculating this, we find:
px = -9768.6 kg·m/s (rounded to one decimal place)
Therefore, the x-component of the car's momentum is -9768.6 kg·m/s.