Track / Stage 4 / 146 of 340 #406 of 2000

Problem 406

AMC 12 late, AIME early

Algebra Difficulty 4.8 Find the answer

4. (20 points) A bullet with a mass of $m=10$ g, flying horizontally at a speed of $v_{1}=400 \mathrm{m} / \mathrm{s}$ , penetrates a massive board and exits with a speed of $v_{2}=100 \mathrm{m} / \mathrm{s}$ . Find the magnitude of the work done on the bullet by the resistance force of the board.

Your answer

Official solution

Answer: 750 J

Solution. From the law of conservation of energy, it follows that

$A=\frac{m v_{1}^{2}}{2}-\frac{m v_{2}^{2}}{2}=\frac{0.01 \cdot 400^{2}}{2}-\frac{0.01 \cdot 100^{2}}{2}=750 \text { J. }$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.