Question

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

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

Step-by-step solution

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 \(23 \mathrm{~m/s}\).

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 = \(69 \mathrm{~m/s}\)

Write the final answer

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

Key concepts

Kinematics

Kinematics is a fundamental branch of physics that deals with the motion of objects without considering the forces that cause this motion. It's like figuring out how something is moving rather than why it's moving, which is essential to understanding basic physics scenarios like our bullet and plank problem.

When we analyze problems using kinematics, we focus on four primary quantities: displacement, velocity, acceleration, and time. For instance, in our bullet problem, we look at changes in speed (a form of velocity)—not worrying about why the bullet changed speed, just calculating the fact of it.

• **Displacement** refers to the change in position of an object.
• **Velocity** is the rate at which an object changes its position.
• **Acceleration** is the rate at which an object changes its velocity.
• **Time** is the period over which motion occurs.

Understanding these concepts helps in tackling various physics problems by providing a framework to quantify motion in a clear, straightforward manner.

Physics Problem Solving

Physics problem solving involves a strategic use of laws and concepts to solve problems effectively. It's like being a detective, using clues given in the problem statement to arrive at a solution. In our bullet scenario, we're applying logical steps to find out what happens to the bullet's velocity.

Here are a few tips for solving physics problems:

• **Understand the Problem**: Read the problem several times to understand what's being asked.
• **Identify Knowns and Unknowns**: In the bullet problem, we know the initial and final speeds of the first bullet and the initial speed of the second bullet.
• **Apply Physics Concepts**: Use the knowns to find the unknown. We use the change in speed of the first bullet to determine what's going to happen to the second one.
• **Calculate Methodically**: Step through your calculations one at a time, paying attention to units and signs.
• **Check Your Answer**: Does your answer make physical sense? Is it consistent with the known principles?

Practicing problem solving builds confidence and enables a deeper understanding of the principles behind the calculations.

Speed and Velocity

Understanding the difference between speed and velocity is crucial for solving any motion-related physics problems. While they may seem similar, they have key differences that can affect your results.

**Speed** is a scalar quantity, meaning it only has magnitude with no direction involved. It simply tells you how fast an object is moving.

**Velocity**, on the other hand, is a vector quantity. This means it not only tells you how fast the object is moving but also in what direction. For instance, wind speed and direction together provide its velocity.

In the given problem, we handled speed changes, which do not include the direction component of velocity. Both initial and final speeds of the bullets are considered to determine their motion through a plank.

To illustrate:

• The **initial speed** of the first bullet is 153 m/s, and its **final speed** is 130 m/s.
• We deduce the speed loss (or reduction) as 23 m/s.
• We apply this speed loss to the second bullet, initially at 92 m/s, ending up with a final speed of 69 m/s.

Being able to differentiate these concepts aids you in precisely understanding and solving tasks according to what aspect of motion they investigate.