A 1000 kilogram car traveling 20.0 meters per second east experiences an impulse of 2000. newton • seconds west. What is the car's final velocity after the impulse has been applied?
To find the car's final velocity after the impulse has been applied, we need to use the impulse-momentum principle, which states that the change in momentum of an object is equal to the impulse applied to it.
The momentum of an object can be calculated using the formula:
momentum (p) = mass (m) × velocity (v)
The initial momentum of the car can be calculated as:
initial momentum = 1000 kg × 20.0 m/s = 20000 kg·m/s east
The change in momentum is equal to the impulse applied, which is given as 2000 N·s west.
So, the final momentum of the car can be calculated as:
final momentum = initial momentum + change in momentum
final momentum = 20000 kg·m/s east + (-2000 N·s west)
To add these two vectors, we need to make sure they have the same direction. Since both the initial momentum and the impulse are given in terms of east and west, we'll keep the answer in this form as well.
final momentum = 20000 kg·m/s east - 2000 N·s west
Now, we can convert the impulse in terms of momentum using the formula:
impulse = change in momentum = final momentum - initial momentum
2000 N·s west = final momentum - 20000 kg·m/s east
To add these vectors, we need to convert the units to the same system. We'll convert N·s to kg·m/s by using the conversion factor that 1 N = 1 kg·m/s².
2000 kg·m/s west = final momentum - 20000 kg·m/s east
Now, we can calculate the final momentum:
final momentum = 20000 kg·m/s east - 2000 kg·m/s west
final momentum = 18000 kg·m/s east - 2000 kg·m/s west
The final velocity of the car can be calculated by dividing the final momentum by the mass of the car:
final velocity = final momentum / mass
final velocity = (18000 kg·m/s east - 2000 kg·m/s west) / 1000 kg
Finally, we combine the east and west terms:
final velocity = (18000 - 2000) m/s east
final velocity = 16000 m/s east
Therefore, the car's final velocity after the impulse has been applied is 16000 m/s east.