Question

a 117 kg rugby player running at 7.75 m/s collides head - on with a padded goalpost and experiences a backward force of 18300 n for 5.50×10^(-2)s. calculate the players final velocity v_f. v_f = m/s question credit: openstax college physics

Explanation:

Step1: Apply the impulse - momentum theorem

The impulse - momentum theorem is \(J = \Delta p\), where \(J = F\Delta t\) (impulse) and \(\Delta p=m(v_{f}-v_{i})\) (change in momentum).
So, \(F\Delta t=m(v_{f}-v_{i})\).

Step2: Rearrange the formula to solve for \(v_{f}\)

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Given \(m = 117\space kg\), \(v_{i}=7.75\space m/s\), \(F=- 18300\space N\) (negative because it's a backward force), \(\Delta t = 5.50\times10^{-2}\space s\)

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Answer:

\(-0.85\space m/s\)