To calculate the force of the hit, we can use the impulse-momentum principle, which states that the change in momentum of an object is equal to the impulse applied to it. Mathematically, it can be expressed as:
Impulse = Change in momentum
The impulse (J) can be calculated using the formula:
J = m * Δv
Where:
J = Impulse
m = Mass of the football player (78 kg)
Δv = Change in velocity
Since the football player comes to a stop after being hit, the change in velocity (Δv) is equal to their initial velocity (-7 m/s). Therefore:
Δv = -7 m/s
The impulse can be further calculated as:
J = m * Δv
= 78 kg * (-7 m/s)
= -546 kg·m/s
The negative sign indicates that the impulse is in the opposite direction to the player's initial velocity.
Now, since impulse is equal to the force multiplied by the contact time (J = F * Δt), we can rearrange the equation to solve for the force (F):
F = J / Δt
Substituting the given values:
F = (-546 kg·m/s) / (0.56 s)
≈ -975 N
The negative sign indicates that the force is in the opposite direction to the player's initial velocity. Therefore, the force of the hit is approximately -975 Newtons.