Chapter 8: Problem 25
A hunter on a frozen, essentially frictionless pond uses a rifle that shoots 4.20-g bullets at 965 m/s. The mass of the hunter (including his gun) is 72.5 kg, and the hunter holds tight to the gun after firing it. Find the recoil velocity of the hunter if he fires the rifle (a) horizontally and (b) at 56.0\(^\circ\) above the horizontal.
Short Answer
Step by step solution
Understand the Law of Conservation of Momentum
Express Conservation of Momentum Mathematically
Solve for Recoil Velocity Horizontally
Analyze the Recoil at an Angle
Solve for Recoil Velocity with Angle
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Physics Problems
The hunter fires a rifle, and this setting clear physics problems involve calculations of velocity and momentum.
By breaking down complex phenomena into simpler parts, physics problems help us delve into the detailed operational workings of physical laws.
- Typically, physics problems require identifying known and unknown quantities.
- They involve using formulas derived from laws or theories of nature, like the law of conservation of momentum in this case.
- Comprehensive problem-solving in physics often involves analyzing different scenarios, such as movement in a horizontal direction or at an angle.
Recoil Velocity
Recoil velocity is evident when the hunter experiences backward momentum upon discharging a bullet forward. It's notable that the velocity is negative indicating opposite direction movement.
Recoil velocity depends on various factors:
- The mass of both the bullet and the shooter (or object experiencing recoil) is key.
- The speed at which the bullet is discharged.
- The angle at which the bullet is fired, affecting how momentum divides between horizontal and vertical components.
Momentum Conservation Formula
This principle is critical in solving the exercise since it explains how the hunter's system behaves post-shot.
The formula used was: \[ m_b \cdot v_b + m_h \cdot v_h = 0 \]
- \(m_b\) is the mass of the bullet, and \(v_b\) is its velocity.
- \(m_h\) is the mass of the hunter (including the gun), and \(v_h\) denotes the recoil velocity.
By implementing this formula, we correctly predict how changes in variables like angle of firing impact the recoil velocity. Understanding this fundamental law allows solving numerous real-world and theoretical physics problems.