Final answer:
To find the magnitude of the final velocity of the 0.145 kg glider in a head-on elastic collision with a 0.291 kg glider, we can use the concept of conservation of momentum. By calculating the initial and final momenta and equating them, we can find the final velocity of the 0.145 kg glider.
Step-by-step explanation:
To find the magnitude of the final velocity of the 0.145 kg glider, we can use the concept of conservation of momentum. In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.
Let's assume the final velocity of the 0.145 kg glider is v. The final momentum of the system will be the sum of the momentum of the 0.145 kg glider and the 0.291 kg glider.
Before the collision, the momentum of the 0.145 kg glider is (0.145 kg) * (0.770 m/s), and the momentum of the 0.291 kg glider is (0.291 kg) * (-2.29 m/s) (since it is moving to the left).
So, the total initial momentum is (0.145 kg) * (0.770 m/s) + (0.291 kg) * (-2.29 m/s).
After the collision, the total final momentum is (0.145 kg + 0.291 kg) * v.
Equating the initial and final momenta, we have (0.145 kg) * (0.770 m/s) + (0.291 kg) * (-2.29 m/s) = (0.145 kg + 0.291 kg) * v.
Solving this equation, we can find the magnitude of the final velocity (v) of the 0.145 kg glider.
Let's go through the calculation:
- First, calculate the initial momentum: (0.145 kg) * (0.770 m/s) + (0.291 kg) * (-2.29 m/s) = result.
- Next, calculate the final momentum: (0.145 kg + 0.291 kg) * v = (0.436 kg) * v.
- Equating the initial and final momenta: result = (0.436 kg) * v.
- Finally, solve for v: v = result / (0.436 kg).
Calculate the value of result, then divide it by (0.436 kg) to find the magnitude of the final velocity (v) of the 0.145 kg glider.