An automobile with a mass of 1450 kg is parked on a moving flatbed railcar; the flatbed is 1.50 m above the ground. The railcar has a mass of 38500 kg and is moving to the right at a constant speed of 8.70 m/s on a frictionless rail. The automobile them accelerates to the left, leaving the railcar at a speed of 22.0 m/s with respect to the ground. When the automobile lands, what is the distance D between it and the left end of the railcar?
t to fall is sqrt(2x/g) = .56
distance car moves = .55*22 = 12.17
rail car moves .55*(8.7)= 4.78
tot = 12.17+4.78
To find the distance D between the automobile and the left end of the railcar when the automobile lands, we can use the concept of conservation of momentum.
1. Begin by calculating the initial momentum of the system (automobile + railcar) before the automobile accelerates. Momentum is given by the equation:
Momentum = mass x velocity
Momentum of the automobile (initially) = mass of the automobile x velocity of the automobile
Momentum of the railcar = mass of the railcar x velocity of the railcar
2. The total momentum of the system before the collision is equal to the total momentum after the collision (due to the law of conservation of momentum), since there is no external force acting on the system:
Total momentum before collision = Total momentum after collision
3. After the automobile accelerates and leaves the railcar, the momentum of the railcar does not change (as there are no external forces). Thus, the momentum of the automobile is equal in magnitude and opposite in direction to the momentum of the railcar:
Momentum of the automobile (final) = - Momentum of the railcar
4. Once you have the final momentum of the automobile, you can calculate the distance D using the equation for momentum:
Momentum = mass x velocity
Rearrange the above equation to solve for velocity:
velocity = Momentum / mass
Since the mass of the automobile is known, divide the final momentum of the automobile by its mass to obtain the final velocity of the automobile.
5. Now, to calculate the time taken by the automobile to land, divide the displacement of the automobile (D) by its final velocity.
time = displacement / velocity
Rearrange the equation to solve for displacement:
displacement = time x velocity
Substitute the final velocity of the automobile obtained in step 4 and the given time (the final velocity of the automobile is achieved when it lands).
6. Finally, substitute the calculated displacement into the equation to get the distance D between the automobile and the left end of the railcar when the automobile lands.