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

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 the padded goalpost exerts on the rugby player = F = -1.81 x 10⁴ N

Negative as it is acting in the opposite direction of the player's initial velocity.

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

Impulse exerted on the rugby player by the goalpost = I

I = FT

Impulse is equal to the change in momentum,

I = MV₂ - MV₁

FT = M(V₂ - V₁)

(-1.81x10⁴)(5.5x10^-2) = (117)(V₂ - 7.95)

-8.51 = V₂ - 7.95

V₂ = -0.56 m/s

Negative sign indicates the rugby player is moving in the opposite direction of the initial velocity after the collision.

Final velocity of the rugby player = -0.56 m/s