Final answer:
To find the new velocity of the train and motorcycle together after collision, the conservation of momentum is applied, yielding a result of approximately 14.2 m/s. The closest provided option should be selected.
Step-by-step explanation:
The subject of this question is Physics, specifically dealing with the concept of conservation of momentum in collisions. Given the masses and initial velocity of the train and the motorcycle, we can calculate the new velocity after the collision assuming an inelastic collision, where both objects move together after the impact.
To find the new velocity, V_f, of the train and motorcycle together, we can use the formula for conservation of momentum:
M1 * V1 + M2 * V2 = (M1 + M2) * Vf
Where:
- M1 is the mass of the train (12,000 kg)
- V1 is the velocity of the train (15.0 m/s)
- M2 is the mass of the motorcycle (700 kg)
- V2 is the velocity of the motorcycle (0 m/s, since it is at rest)
Substituting the values into the equation:
(12,000 kg * 15.0 m/s + 700 kg * 0 m/s) = (12,000 kg + 700 kg) * Vf
180,000 kg*m/s = 12,700 kg * Vf
Dividing both sides by the total mass gives:
Vf = 180,000 kg*m/s / 12,700 kg = 14.173 m/s
After rounding to two decimal places, the new velocity is approximately 14.2 m/s. However, as this answer is not exactly matching any of the provided options and is given with approximation, please check against the available options for the closest match or re-evaluate the calculation if necessary.