High School

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Which person or object has the greatest quantity of motion? Circle your answer.

a. The 142 kg baseball moving at 40 m/s the instant before it makes contact with the catcher’s glove.

b. The swimmer from question 1 (70 kg) at the instant she leaves the starting platform.

c. Nicole, the 70 kg volleyball player from question 2, the instant before her feet first touch the floor after the serve when her velocity was 4.0 m/s downward.

d. A 114 kg football lineman standing at rest before the football is snapped.

Answer :

Option (a) the 142 kg baseball moving at 40 m/s the instant before it makes contact with the catcher’s glove has the greatest quantity of motion.

To determine which person or object has the greatest quantity of motion, we can calculate the momentum for each option. Momentum is defined as the product of an object's mass and its velocity. The greater the momentum, the greater the quantity of motion.

a. Momentum of the baseball:

[tex]\[ Momentum = \text{Mass} \times \text{Velocity} = 142 \, \text{kg} \times 40 \, \text{m/s} = 5680 \, \text{kg} \cdot \text{m/s} \][/tex]

b. Momentum of the swimmer:

[tex]\[ Momentum = \text{Mass} \times \text{Velocity} = 70 \, \text{kg} \times (\text{speed at which she leaves the starting platform}) \][/tex]

Since we don't have the speed at which she leaves the platform, we can't calculate the momentum for this option.

c. Momentum of Nicole:

[tex]\[ Momentum = \text{Mass} \times \text{Velocity} = 70 \, \text{kg} \times 4.0 \, \text{m/s} = 280 \, \text{kg} \cdot \text{m/s} \][/tex]

d. Momentum of the football lineman:

[tex]\[ Momentum = \text{Mass} \times \text{Velocity} = 114 \, \text{kg} \times 0 \, \text{m/s} = 0 \, \text{kg} \cdot \text{m/s} \][/tex]

Now, comparing the calculated momenta:

a. Momentum of the baseball: [tex]\( 5680 \, \text{kg} \cdot \text{m/s} \)[/tex]

c. Momentum of Nicole: [tex]\( 280 \, \text{kg} \cdot \text{m/s} \)[/tex]

d. Momentum of the football lineman: [tex]\( 0 \, \text{kg} \cdot \text{m/s} \)[/tex]

Therefore, option (a) the 142 kg baseball moving at 40 m/s the instant before it makes contact with the catcher’s glove has the greatest quantity of motion.

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