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Chapter 4: Problem 14

A bullet losses \(19 \%\) of its kinetic energy when passes through an obstacle. The percentage change in its speed is (A) Reduced by \(10 \%\) (B) Reduced by \(19 \%\) (C) Reduced by \(9.5 \%\) (D) Reduced by \(11 \%\)

Short Answer

Expert verified
The percentage change in the bullet's speed is approximately 10%. So, the correct answer is (A) Reduced by 10%.

Step by step solution

01

Write the initial and final kinetic energy equations

We know that the initial kinetic energy is given by: KE_initial = \(\frac{1}{2}mv^2\), where m is the mass of the bullet and v is its initial speed. After passing through the obstacle, the bullet loses 19% of its kinetic energy, so the final kinetic energy is 81% of the initial kinetic energy: KE_final = 0.81 * KE_initial. The final kinetic energy can also be expressed as: KE_final = \(\frac{1}{2}mv'^2\), where v' is the final speed of the bullet.
02

Set up the equation and solve for the final speed

Since KE_final = 0.81 * KE_initial, we can write: \(\frac{1}{2}mv'^2\) = 0.81 * \(\frac{1}{2}mv^2\). The mass and the factor of 1/2 can be canceled on both sides, leaving us with: \(v'^2\) = 0.81 * \(v^2\). Now, let's find the final speed, v': \(v'\) = \(v\sqrt{0.81}\).
03

Calculate the percentage change in speed

The percentage change in speed is given by: percentage change = \(\frac{v - v'}{v} * 100\). Substituting the expression for the final speed, v', we have: percentage change = \(\frac{v - v\sqrt{0.81}}{v} * 100\). The initial speed, v, can be canceled out on both the numerator and the denominator, leaving us with: percentage change = \(\frac{1 - \sqrt{0.81}}{1} * 100\). Evaluating this expression: percentage change 鈮� 10%. The percentage change in the bullet's speed is approximately 10%. So, the correct answer is (A) Reduced by 10%.

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