Final answer:
The rugby player's final speed, after colliding with the goalpost and experiencing a backward force, is -2.8 m/s, indicating he is moving backward. The opponent struck by a boxer will have a final velocity of 2 m/s after the punch.
Step-by-step explanation:
Calculating Final Speed After Collision for Rugby Player
To calculate the final speed of the 110-kg rugby player, we must first determine the impulse exerted on him. Impulse is equal to the change in momentum and is calculated using the equation Impulse = Force × Time. In this case, the backward force exerted is 1.76 × 10⁴ N for a duration of 5.50 × 10⁻² s.
Impulse = (1.76 × 10⁴ N) × (5.50 × 10⁻² s) = 968 N·s
Since this is a backward force, it will reduce the player's forward momentum. The player's initial momentum is given by mass × initial velocity, which is (110 kg) × (6 m/s) = 660 kg·m/s. Subtracting the impulse from the initial momentum gives us the final momentum:
Final momentum = Initial momentum - Impulse = 660 kg·m/s - 968 N·s = -308 kg·m/s
The final velocity can be found by dividing the final momentum by the mass of the player:
Final velocity = Final momentum / mass = -308 kg·m/s / 110 kg = -2.8 m/s
This means the player is now moving backward after the collision at a speed of 2.8 m/s.
Calculating Opponent's Final Velocity from Boxer's Punch
Next, we calculate the opponent's final velocity after being struck by a professional boxer. The force of the punch is 1050 N, and it lasts for 0.20 s. Using the same impulse formula (Impulse = Force × Time) we get:
Impulse = (1050 N) × (0.20 s) = 210 N·s
As the opponent was initially at rest (initial velocity = 0 m/s), the final momentum is equal to the impulse:
Final momentum = 210 N·s
To find the final velocity, we divide this by the mass of the opponent:
Final velocity = Final momentum / mass = 210 N·s / 105 kg = 2 m/s
The opponent will have a final velocity of 2 m/s after the punch.