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? solve this
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object is given by the product of its mass (m) and its velocity (v): p = mv.
Before the collision:
The momentum of the truck (m1v1) is 2000 kg * 40 m/s = 80000 kg*m/s (Westward direction).
After the collision:
Let's denote the mass of the car (m2) and its final velocity (v2).
The momentum of the car (m2v2) is determined by the impulse (I), which is given by the product of the force (F) and the time (t) it acts on the car:
I = Ft
In the given problem, the impulse is 8000 N*s in the eastward direction. We know that impulse and change in momentum are equal, so we can write:
m2v2 = I
m2v2 = 8000 N*s
Since the initial momentum of the truck is in the Westward direction, and the impulse is in the Eastward direction, the final momentum should be in the Eastward direction as well.
Now, we can solve for the final velocity (v2):
v2 = I / m2
v2 = 8000 N*s / m2
To find the mass of the car (m2), we can use the principle of conservation of momentum:
m1v1 = m2v2
2000 kg * 40 m/s = m2 * v2
Substituting the expression for v2:
2000 kg * 40 m/s = m2 * (8000 N*s / m2)
Now, we can simplify and solve for m2:
80000 kg*m/s = 8000 N*s
m2 = 80000 kg*m/s / (8000 N*s)
m2 = 10 kg
Now that we have found the mass of the car (m2 = 10 kg), we can find the value of v2 by substituting it back into the equation:
v2 = 8000 N*s / (10 kg)
v2 = 800 m/s
Therefore, the final velocity of the car after the accident is 800 m/s to the East.