Final answer:
Using the conservation of momentum, the speed of the second drone car after the collision is calculated to be 9.6 m/s, which is not one of the options provided, suggesting there might be a typo in the question or a mistake in the provided options.
Step-by-step explanation:
To find the speed of the other drone car after the collision, we need to use the conservation of momentum principle, which states that the total momentum before the collision is equal to the total momentum after the collision. The situation described is a one-dimensional collision, so we can use the formula:
Momentum before = m1∗v1 + m2∗v2
Momentum after = m1∗v1' + m2∗v2'
Where:
m1 = 1000 kg (mass of the first car),
v1 = 12 m/s (initial speed of the first car),
m2 = 500 kg (mass of the second car, half the mass of the first),
v2 = -17 m/s (initial speed of the second car, negative sign indicates opposite direction),
m1' = 1000 kg (mass of the first car after collision),
v1' = -1.3 m/s (speed of the first car after collision, negative sign indicates opposite direction),
m2' = 500 kg (mass of the second car after collision),
v2' is the unknown we are solving for.
Substituting the known values into the momentum before and after equation, we get:
1000 kg ∗ 12 m/s + 500 kg ∗ (-17 m/s) = 1000 kg ∗ (-1.3 m/s) + 500 kg ∗ v2'
After calculating the momenta and simplifying:
12000 kg∗m/s - 8500 kg∗m/s = -1300 kg∗m/s + 500 kg ∗ v2'
This simplifies to:
3500 kg∗m/s = -1300 kg∗m/s + 500 kg ∗ v2'
Finding v2' then gives us:
500 kg ∗ v2' = 4800 kg∗m/s
v2' = 9.6 m/s
Therefore, the speed of the second drone car after the collision is 9.6 m/s, which is not listed in the options provided by the student. This might indicate a typo in the question, or a mistake in the options presented.