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Chapter 5: Problem 33

A bullet moving at a speed of \(153 \mathrm{~m} / \mathrm{s}\) passes through a plank of wood. After passing through the plank, its speed is \(130 \mathrm{~m} / \mathrm{s}\). Another bullet, of the same mass and size but moving at \(92 \mathrm{~m} / \mathrm{s}\), passes through an identical plank. What will this second bullet's speed be after passing through the plank? Assume that the resistance offered by the plank is independent of the speed of the bullet.

Short Answer

Expert verified
Answer: The speed of the second bullet after passing through the plank will be \(69 \mathrm{~m/s}\).

Step by step solution

01

Calculate the change in speed for the first bullet

First, find the change in speed for the first bullet by subtracting its final speed from its initial speed: Change in speed = Initial speed - Final speed Change in speed = \(153 \mathrm{~m/s} - 130 \mathrm{~m/s}\) Change in speed = \(23 \mathrm{~m/s}\) The change in speed for the first bullet is \(23 \mathrm{~m/s}\).
02

Apply the change in speed to the second bullet

Now, we can apply the same change in speed to the second bullet. Since the bullet slows down after passing through the plank, subtract the change in speed from the second bullet's initial speed to find its final speed: Final speed of the second bullet = Initial speed of the second bullet - Change in speed Final speed of the second bullet = \(92 \mathrm{~m/s} - 23 \mathrm{~m/s}\) Final speed of the second bullet = \(69 \mathrm{~m/s}\)
03

Write the final answer

After passing through the plank, the speed of the second bullet will be \(69 \mathrm{~m/s}\).

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