Final answer:
The original momentum of the 95-kg fullback running at 3.0 m/s was 285 kg·m/s to the east. The impulse exerted on the fullback (and by Newton's third law, also on the tackler) was 285 kg·m/s in magnitude, with the fullback's being eastward and the tackler's westward. The average force exerted on the tackler was 335.29 N westward.
Step-by-step explanation:
The student is asking about concepts related to momentum and impulse in physics, particularly as they apply to a situation involving a football player. The subject of this question is Physics and it is typically covered at the High School level. Let's calculate each part step by step:
(a) The Original Momentum of the Fullback
The momentum of an object is calculated as the product of its mass and its velocity. The formula for momentum (p) is:
p = m × v
where:
- m is the mass of the fullback (95 kg)
- v is the velocity of the fullback (3.0 m/s east)
Thus, the original momentum of the fullback is:
p = 95 kg × 3.0 m/s
= 285 kg·m/s (east)
(b) The Impulse Exerted on the Fullback
Impulse is equal to the change in momentum or can be calculated as the product of the average force (F) exerted during the time interval (Δt) the force acts. The formula for impulse (J) is:
J = F × Δt
Since we know the fullback was stopped, the final momentum is 0 kg·m/s. The change in momentum is the final momentum minus the initial momentum:
Δp = 0 kg·m/s - 285 kg·m/s
= -285 kg·m/s
Thus, the impulse exerted on the fullback is -285 kg·m/s, which is the negative of the initial momentum because the fullback has been brought to a stop, indicating a change in the opposite direction.
(c) The Impulse Exerted on the Tackler
By Newton's third law of motion, the impulse exerted on the tackler will be equal in magnitude but opposite in direction to the impulse exerted on the fullback. Thus, the impulse exerted on the tackler is:
+285 kg·m/s (west)
(d) The Average Force Exerted on the Tackler
To find the average force exerted on the tackler, we use the impulse and the time interval:
F = J / Δt
Substituting in the values, we get:
F = 285 kg·m/s / 0.85 s
= 335.29 N (west)