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A softball player hits a ball at 78 miles per hour. Then she hits a ball at 80 miles per hour. Which is the best prediction?(1...Question
A softball player hits a ball at 78 miles per hour. Then she hits a ball at 80 miles per hour. Which is the best prediction? (1 point)
• The ball hit at 80 miles per hour will have more kinetic energy.
• The balls' kinetic energies will depend on the distances they travel.
• The balls will have the same amount of kinetic energy.
• The ball hit at 78 miles per hour will have more kinetic energy.
• The ball hit at 80 miles per hour will have more kinetic energy.
• The balls' kinetic energies will depend on the distances they travel.
• The balls will have the same amount of kinetic energy.
• The ball hit at 78 miles per hour will have more kinetic energy.
Answers
GPT-4o mini
To determine which ball has more kinetic energy, we use the formula for kinetic energy (KE):
\[ \text{KE} = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the object and \( v \) is its velocity.
Since both balls are hit by the same player and are likely to be similar in mass, we can ignore the mass in our comparison. The kinetic energy will therefore depend primarily on the square of the velocity.
1. For the ball hit at 78 miles per hour:
\[ \text{KE}_{78} = \frac{1}{2} m (78)^2 \]
2. For the ball hit at 80 miles per hour:
\[ \text{KE}_{80} = \frac{1}{2} m (80)^2 \]
Comparing the two:
- \( (80)^2 = 6400 \)
- \( (78)^2 = 6084 \)
Since \( 6400 > 6084 \), the ball hit at 80 miles per hour will have more kinetic energy than the ball hit at 78 miles per hour.
Thus, the best prediction is:
• The ball hit at 80 miles per hour will have more kinetic energy.
\[ \text{KE} = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the object and \( v \) is its velocity.
Since both balls are hit by the same player and are likely to be similar in mass, we can ignore the mass in our comparison. The kinetic energy will therefore depend primarily on the square of the velocity.
1. For the ball hit at 78 miles per hour:
\[ \text{KE}_{78} = \frac{1}{2} m (78)^2 \]
2. For the ball hit at 80 miles per hour:
\[ \text{KE}_{80} = \frac{1}{2} m (80)^2 \]
Comparing the two:
- \( (80)^2 = 6400 \)
- \( (78)^2 = 6084 \)
Since \( 6400 > 6084 \), the ball hit at 80 miles per hour will have more kinetic energy than the ball hit at 78 miles per hour.
Thus, the best prediction is:
• The ball hit at 80 miles per hour will have more kinetic energy.