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One particular lion (Panthera leo) with a mass of 143 kg, is observed to reach a speed of 80.5 km/h in 5.7 s. What is the magnitude of the work (in kJ) done by this lion?

Answer :

The magnitude of the work done by the lion is 35.75 kJ.

To calculate the work done by the lion, we need to determine the kinetic energy it gains. The formula for kinetic energy (\( KE \)) is:

[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]

where:

  • m is the mass of the lion (143 kg),
  • v is the final velocity.

First, convert the velocity from km/h to m/s:

[tex]\[ 80.5 \text{ km/h} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{3600 \text{ s}} = 22.36 \text{ m/s} \][/tex]

Now, calculate the kinetic energy:

[tex]\[ KE = \frac{1}{2} \times 143 \text{ kg} \times (22.36 \text{ m/s})^2 \][/tex]

[tex]\[ KE = \frac{1}{2} \times 143 \times 499.97 \][/tex]

[tex]\[ KE = 35,747.9 \text{ J} \][/tex]

Convert this to kilojoules (kJ):

[tex]\[ 35,747.8 \text{ J} \div 1000 = 35.75 \text{ kJ} \][/tex]

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