A 2000 kg truck is traveling west with a speed of 40 meters per second when it strikes another car, creating an impulse of 8000 Newtons●seconds in the eastward direction. What is the final velocity and direction for the car after the accident? a. 33.5 m/s going east b. 39.75 m/s going west c. 27.6 m/s going west d. 36 m/s going east
To solve this problem, we can use the principle of conservation of momentum.
The initial momentum of the truck is given by:
Momentum = Mass * Velocity = 2000 kg * 40 m/s = 80000 kg*m/s to the west
The impulse experienced by the truck is given by:
Impulse = Force * Time = 8000 N*s to the east
According to the principle of conservation of momentum, the total momentum before and after the collision should be equal.
Total momentum before = Total momentum after
80000 kg*m/s (initial momentum of the truck) = (Mass of truck + Mass of car) * Final velocity
Final velocity = 80000 kg*m/s / (2000 kg + Mass of car)
Assuming the mass of the car is negligible compared to the truck, we can simplify the equation:
Final velocity ≈ 80000 kg*m/s / 2000 kg
Final velocity ≈ 40 m/s
Thus, the final velocity of the car after the accident is 40 m/s going west.
Therefore, the correct answer is c. 27.6 m/s going west.