Final answer:
By applying the conservation of momentum to the two-car collision and solving for the unknown final velocity of the second car, we find that the other drone car's speed after the collision should be 9.6 m/s. However, this answer is not one of the options provided, suggesting an error in the question.
Thus the corret opction is:d
Step-by-step explanation:
The question involves applying the law of conservation of momentum to a collision between two cars.
According to this law, the total momentum of a system of objects is conserved if no external forces act on the system.
In a collision where external forces can be neglected, like the one described, the momentum before and after the collision will be the same.
To find the speed of the other drone car after the collision, we can set up the equation using the conservation of momentum as follows:
m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2'
Where:
- m1 is the mass of the first car (1000kg)
- v1 is the initial velocity of the first car (12 m/s)
- m2 is the mass of the second car (500kg)
- v2 is the initial velocity of the second car (-17 m/s)
- v1' is the final velocity of the first car (-1.3 m/s)
- v2' is the final velocity of the second car (what we are solving for)
Plugging in the known values:
1000kg * 12 m/s + 500kg * (-17 m/s) = 1000kg * (-1.3 m/s) + 500kg * v2'
12000 kg*m/s - 8500 kg*m/s = -1300 kg*m/s + 500kg * v2'
3500 kg*m/s = -1300 kg*m/s + 500kg * v2'
4800 kg*m/s = 500kg * v2'
v2' = 4800 kg*m/s / 500kg
v2' = 9.6 m/s
Thus, the speed of the other drone car after the collision is 9.6 m/s, which is not one of the options provided. This indicates that there may have been an error in the options given or in the initial conditions provided.