Final answer:
To find the bicycle speed immediately after Tony throws his pack, we can apply the principle of conservation of momentum. The total initial momentum of the bicycle and Tony is equal to the total final momentum, so we can set up an equation and solve for the final velocity of the bicycle. The bicycle speed immediately after the throw is 3 m/s.
Step-by-step explanation:
To solve this problem, we can apply the principle of conservation of momentum. The initial momentum of the system is equal to the final momentum of the system. In this case, the system consists of the bicycle and Tony, so we need to calculate the initial and final momentum of the bicycle and Tony together.
The initial momentum of the system is the sum of the individual momenta before the throw. Tony's initial momentum is given by: momentum = mass * velocity = 50 kg * 3 m/s = 150 kg·m/s. The bicycle's initial momentum is given by: momentum = mass * velocity = 10 kg * 3 m/s = 30 kg·m/s. The total initial momentum of the system is therefore 150 kg·m/s + 30 kg·m/s = 180 kg·m/s.
After Tony throws the pack forward, the pack will have its own initial momentum. However, since Tony and the bicycle are still connected, the total momentum of the system must remain the same. The final momentum of the system is therefore 180 kg·m/s. We can now calculate the final momentum of the bicycle and Tony together. Let's denote the final velocity of the bicycle as vf. The final momentum of the bicycle and Tony is given by: momentum = (mass of bicycle + mass of Tony) * final velocity = (10 kg + 50 kg) * vf = 60 kg * vf.
Since the total momentum of the system is equal to 180 kg·m/s, we can set the equation 60 kg * vf = 180 kg·m/s and solve for vf. Dividing both sides of the equation by 60 kg gives vf = 180 kg·m/s / 60 kg = 3 m/s.