Final answer:
To find the final velocity of Chad and Cindy after an inelastic collision, conservation of momentum is used. Their combined mass and the sum of their individual momenta are calculated, resulting in a final velocity of approximately 7 m/s, which rounds to 7 m/s, matching option C).
Step-by-step explanation:
The student's question involves a collision between two ice skaters, Chad and Cindy, which is a classic example of a conservation of momentum problem in physics. To find the final velocity (Vf) after their inelastic collision, we can use the principle of conservation of linear momentum, which states that the total momentum before the collision equals the total momentum after the collision when no external forces are acting on the system.
The formula to calculate the final velocity after an inelastic collision when two objects stick together is:
Momentum before collision = Momentum after collision
m1×v1 + m2×v2 = (m1 + m2)×Vf
Where:
- m1 is the mass of Chad (77 kg),
- v1 is the velocity of Chad (8 m/s),
- m2 is the mass of Cindy (52 kg),
- v2 is the velocity of Cindy (5 m/s), and
- Vf is the final velocity of Chad and Cindy together.
Plugging the values into the equation:
77 kg × 8 m/s + 52 kg × 5 m/s = (77 kg + 52 kg) × Vf
616 kg×m/s + 260 kg×m/s = 129 kg × Vf
876 kg×m/s = 129 kg × Vf
Now, let's solve for Vf:
Vf = 876 kg×m/s / 129 kg
Vf ≈ 6.79 m/s
Rounding to the nearest whole number, we get 7 m/s as the final velocity, which corresponds to option C).