Final answer:
The velocity of a 900-kg car initially moving at 30.0 m/s, just after it hits a 150-kg deer running at 12.0 m/s in the same direction with the assumption that the deer remains on the car, would be 27.4 m/s when calculated with three significant figures. The question's information on preventing a collision is not addressed due to a possible error in question formulation.
Step-by-step explanation:
To solve for the maximum speed the car could have to avoid hitting the deer, we can use the conservation of momentum since the question provides the mass and initial speed of both the car and the deer. However, it seems like there might be confusion in the problem statement. The question provided speaks more about the velocity of the car just after an impact, assuming the deer remains on the car, rather than preventing the collision. To address this correctly, we'll first find the velocity after impact and then clarify the concept of maximum speed to avoid collision.
Using the conservation of momentum:
So, calculating the after-impact velocity:
Momentum before impact = (900 kg × 30.0 m/s) + (150 kg × 12.0 m/s) = 27000 kg·m/s + 1800 kg·m/s = 28800 kg·m/s
After impact, the mass is 900 kg + 150 kg = 1050 kg.
So, the velocity after impact is:
Momentum after impact / total mass = 28800 kg·m/s / 1050 kg = 27.43 m/s
To match the requirement of three significant figures, the velocity after impact is 27.4 m/s.
If the question were about the maximum speed to avoid hitting the deer, we would need additional information, such as the distance of the car from the deer upon sighting and the reaction time of the driver.