The boy B jumps off the canoe at A with a velocity of relative to the canoe as – [Free] B51
The boy B jumps off the canoe at A with a velocity of π£ π΅ / π΄ = 4.5 m/s v B/A β =4.5m/s relative to the canoe as shown in (Figure 1). He lands in the second canoe C. Each canoe has a mass of 40 kg. The boyβs mass is 35 kg, and the girl D has a mass of 25 kg. Both canoes are originally at rest. Part A Determine the final speed of canoe A after the motion. Express your answer to three significant figures and include the appropriate units. Part B Determine the final speed of canoe C after the motion. Express your answer to three significant figures and include the appropriate units. Would you like me to double-check the previous solution based on this wording?
Answer
π£ Canoe Momentum Conservation Problem
β Step 1: Initial Momentum Analysis
Initially, both Canoe A and the boy are at rest:
- Mass of Canoe A = 40 kg
- Mass of Boy = 35 kg
- Boy’s velocity relative to Canoe A: vB/A = 4.5 m/s
Let:
- vA = Velocity of Canoe A after recoil (negative means left)
- vB = Velocity of boy relative to ground
Apply conservation of momentum:
β 0 = 35(vA + 4.5) + 40vA
Solving:
β vA = -2.1 m/s
β Step 2: Boyβs Velocity Relative to Ground
Boy moves at 2.4 m/s forward.
β Step 3: Boy Lands in Canoe C
- Mass of Canoe C = 40 kg
- Mass of Girl = 25 kg
- Total mass after boy lands = 100 kg
Momentum before impact (boy only):
Apply conservation of momentum:
πΉ Final Speed of Canoe C: 0.84 m/s (forward)