A 3000 kg car is traveling west with a speed of 30 meters per second when it strikes another car, creating an impulse of 7000 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. 26.5 m/s going east c. 27.6 m/s going west d. 233.3 m/s going west
To find the final velocity of the car after the accident, we can use the impulse-momentum principle, which states that the impulse applied to an object is equal to the change in momentum of the object.
The impulse is given as 7000 Newtons●seconds in the eastward direction. Since impulse is the product of force and time, we can calculate the force applied to the car using the equation:
force = impulse / time
Given that the impulse is 7000 Newtons●seconds, and the time is 1 second (since it is not specified in the question), the force can be calculated as:
force = 7000 N●s / 1 s = 7000 Newtons
Now, let's consider the change in momentum of the car. The initial momentum is the product of mass and initial velocity:
initial momentum = mass * initial velocity
= 3000 kg * 30 m/s
= 90000 kg m/s
The final momentum can be calculated using the equation:
final momentum = initial momentum + impulse
final momentum = 90000 kg m/s + 7000 N●s
= 97000 kg m/s
Since momentum is equal to the product of mass and velocity, we can calculate the final velocity as:
final velocity = final momentum / mass
= 97000 kg m/s / 3000 kg
≈ 32.33 m/s
The final velocity is approximately 32.33 m/s. Since the initial velocity is in the westward direction, the final velocity will also be in the same direction.
Thus, the correct answer is:
d. 32.33 m/s going west