High School

Calculate the final velocity of a 118 kg rugby player who is initially running at 7.45 m/s and collides head-on with a padded goalpost, experiencing a backward force of 17,500 N for [tex]5.50 \times 10^{-2} \text{ s}[/tex].

Final velocity: _________ m/s

Answer :

The final velocity of the rugby player is 3.95 m/s in backward direction.

How to calculate the final velocity of the player?

The final velocity of the player is calculated by applying the following formula as shown below.

The impulse experienced by the player is;

J = Ft

where;

  • F is force
  • t is time

J = 7500 N × 5.50 × 10⁻² s

J = 412.5 Ns

The final velocity is calculated using change in momentum formula;

J = ΔP

ΔP = m(v - (-u)

v + u = ΔP / m

v = ΔP / m - u

v = 412.5 / 118 - 7.45

v = -3.95 m/s

Thus, the final velocity of the rugby player is 3.95 m/s in backward direction.

Final answer:

To find the final velocity, we use the impulse-momentum theorem. By calculating the impulse and the change in momentum, we determined that the rugby player will have a final velocity of -0.715 m/s, meaning they will be moving backward after the collision.

Explanation:

To calculate the final velocity of the rugby player after the collision, we use the impulse-momentum theorem. The impulse experienced by the player is the product of the average force exerted on him and the time interval over which it is applied. Given a backward force of 17500 N for a duration of 5.50 x 10^{-2} s and an initial velocity of 7.45 m/s, the impulse can be calculated. Impulse causes a change in momentum, so we can express this as:

Impulse = Force x time = Change in momentum

Impulse = 17500 N x 5.50 x 10^{-2} s = 962.5 kg x m/s

Now, we find the change in momentum:


Change in momentum = final momentum - initial momentum

Since initial momentum = mass x initial velocity:


Initial momentum = 118 kg x 7.45 m/s = 878.1 kg x m/s

Now, we can find the final momentum by subtracting the impulse (change in momentum) from the initial momentum, since the force is backward:


Final momentum = initial momentum - impulse


Final momentum = 878.1 kg x m/s - 962.5 kg x m/s = -84.4 kg x m/s

Since final momentum = mass x final velocity, we can find the final velocity by dividing the final momentum by the mass of the player:


Final velocity = Final momentum / mass


Final velocity = -84.4 kg x m/s / 118 kg = -0.715 m/s

Since the final velocity is negative, it indicates that the player is moving backwards after the collision.

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