A 57.6 kg pole-vaulter falls from rest from a height of 5.4 m onto a foam-rubber pad. The pole-vaulter comes to rest 0.34 s after landing on the pad.

Question

(a) Calculate the athlete's velocity just before reaching the pad.

(b) Calculate the constant force exerted on the pole-vaulter due to the collision.

Answer 1

For part (a) you can use the equation of motion v² = u² + 2as, where u = 0 (starting at rest), or you can apply conservation of mechanical energy, which will also yield v² = 2as.

v² = (2)(9.81)(5.4) = 105.9 m²/s² ⇒ v = 10.3 m/s.

For part (b), use the impulse-momentum relationship

F = Δp / Δt = m(v - u) / Δt, where the initial speed (u) is the answer from (a), the final speed (v) is 0 (at rest), and Δt is 0.34s.

F = m(v - u) / Δt = (57.6 (0 - 10.3) / 0.34) kg m s^-2 = - 593 N