Final answer:
To calculate the final velocity of a rugby player post-collision using the impulse-momentum theorem, the given force and time are used to find the impulse, which equals the change in momentum. The change in velocity is found by dividing the impulse by the player's mass, leading to a final velocity of approximately -0.63 m/s, indicating backward motion.
Step-by-step explanation:
The subject of this question is Physics, specifically involving concepts of mechanics such as momentum and impulse, which are part of a typical high school physics curriculum.
Calculation of Final Velocity
To calculate the final velocity of the rugby player after colliding with the goalpost, we can use the impulse-momentum theorem. This theorem states that an impulse on an object is equal to the change in the object's momentum.
The impulse exerted on the player can be calculated using the formula:
Impulse (J) = Force (F) × Time (t)
For our rugby player:
J = (1.75×10⁴ N) × (5.35×10⁻² s)
This is the product of the backward force and the time for which the force acts. This gives us the impulse in Newton-seconds (Ns).
The change in momentum (Δp) is equal to the impulse:
Δp = J
Δp = mΔv
Where m is the mass of the rugby player and Δv is the change in velocity. We can calculate Δv by rearranging the formula:
Δv = J/m
The initial velocity (v_i) of the rugby player is given as 7.5 m/s in the positive direction, and the final velocity (v_f) will be the initial velocity plus the change in velocity (noting that the impulse will cause a decrease in velocity since it acts in the opposite direction):
v_f = v_i - Δv
Substitute the values to find v_f, and keep in mind that the final velocity might be negative if the player is pushed backwards.
With actual calculation:
J = (1.75×10⁴ N) × (5.35×10⁻² s) = 935.25 Ns
Δv = 935.25 Ns / 115 kg = 8.13 m/s (approx)
v_f = 7.5 m/s - 8.13 m/s = -0.63 m/s (approx)
The negative sign indicates the player is moving in the opposite direction after the collision.
Final Result
The final velocity of the rugby player in the horizontal direction after the collision is approximately -0.63 m/s.