Question

Calculate the final velocity right after a 117-kg rugby player who is initially running at 7.95 m/s collides head-on with a padded goalpost and experiences a backward force of 1.81 × 104 N for 5.50 × 10-2 s.

Answer 1

Let us consider the direction of the initial velocity of the rugby player as positive.

Mass of the rugby player = m = 117 kg

Initial velocity of the rugby player = V₁ = 7.95 m/s

Final velocity of the rugby player = V₂

Force exerted by the goalpost on the rugby player = F = -1.81 x 10⁴ N = -18100 N

The force is negative as it acts in the opposite direction of the initial velocity of the rugby player.

Time period = T = 5.5 x 10^-2 sec

The impulse of the force is equal to the change in momentum of the rugby player.

FT = mV₂ - mV₁

FT = m(V₂ - V₁)

(-18100)(5.5x10^-2) = (117)(V₂ - 7.95)

-8.508 = V₂ - 7.95

V₂ = -0.558 m/s

The negative sign indicates that the rugby player is moving in the direction opposite to the initial velocity.

Final velocity of the rugby player = -0.558 m/s