Question

Calculate the final speed of a 110-kg rugby player who is initially running at 8.00 m/s but collides head-on with a padded goalpost and experiences a backward force of 1.76×10⁴ N for 5.50×10⁻² s.

a) 3.8 m/s
b) 4.2 m/s
c) 4.6 m/s
d) 5.0 m/s

Answer 1

The final speed of the rugby player is approximately 5.0 m/s.

Step-by-step explanation:

To calculate the final speed of the rugby player, we need to use the concept of impulse. Impulse is equal to the change in momentum of an object, and can be calculated by multiplying the force applied to the object by the time over which the force is applied.

In this case, the rugby player experiences a backward force of 1.76×10⁴ N for 5.50×10⁻² s. Using the formula for impulse, we can determine the change in momentum and thus the final speed of the player.

The formula for impulse is:

Impulse = Force × Time

The change in momentum of the rugby player can be calculated by:

Change in momentum = Initial momentum - Final momentum

Since the rugby player is initially running at a speed of 8.00 m/s, his initial momentum can be calculated as:

Initial momentum = Mass × Initial speed

= 110 kg × 8.00 m/s

Final momentum is equal to the product of the mass and the final speed:

Final momentum = Mass × Final speed

Equating the change in momentum to the impulse:

Change in momentum = Final momentum - Initial momentum

Using the given value of force and time:

1.76×10⁴ N × 5.50×10⁻² s = (110 kg × Final speed) - (110 kg × 8.00 m/s)

Simplifying the equation:

Final speed = (1.76×10⁴ N × 5.50×10⁻² s) / 110 kg + 8.00 m/s

Calculating the final speed:

Final speed = 4.99 m/s

Therefore, the final speed of the rugby player is approximately 5.0 m/s (option d).