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Question 26
A tennis ball has a mass of 58 g. The ball is dropped from rest from a height of 1.8 m above the ground and falls vertically. The ball rebounds vertically to a heigh... show full transcript
Step 1
Answer
First, we will convert the mass of the tennis ball from grams to kilograms: 58 g = 0.058 kg.
Next, we calculate the velocity of the ball just before it hits the ground using the formula for gravitational potential energy and kinetic energy:
Potential energy at height 1.8 m is converted to kinetic energy just before impact:
Solving for the velocity, we use:
Substituting the values, we get:
Thus, the momentum just before hitting the ground is: $$p = mv = 0.058 \times 5.88 = 0.341 ext{ kg m/s}.$
Step 2
Answer
Now, we calculate the momentum of the ball just after rebounding to a height of 1.1 m:
Similarly, the velocity just after rebounding can be calculated using:
Substituting the values, we find:
Thus, the momentum just after rebounding is: $$p' = mv' = 0.058 \times 4.67 = 0.271 ext{ kg m/s}.$
Step 3
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