Two particles are fired together along a smooth horizontal surface with velocities 4 m/s and...
FURTHER MATHEMATICS
WAEC 2010
Two particles are fired together along a smooth horizontal surface with velocities 4 m/s and 5 m/s. If they move at 60° to each other, find the distance between them in 2 seconds.
- A. \(2\sqrt{61}\)
- B. \(\sqrt{42}\)
- C. \(2\sqrt{21}\)
- D. \(2\sqrt{10}\)
Correct Answer: C. \(2\sqrt{21}\)
Explanation
Given lines \(OA\) and \(OB\) inclined at angle \(\theta\), the line \(AB\) is gotten using cosine rule.
\(|AB|^{2} = |OA|^{2} + |OB|^{2} - 2|OA||OB|\cos \theta\)
\(|AB|^{2} = 4^{2} + 5^{2} - 2(4)(5)\cos 60\)
= \(16 + 25 - 20\)
\(|AB|^{2} = 21 \implies |AB| = \sqrt{21}\)
\(\implies \text{The two particles are} \sqrt{21} m \text{apart in 1 sec}\)
In two seconds, the particles will be \(2\sqrt{21} m\) apart.
Post an Explanation Or Report an Error
If you see any wrong question or answer, please leave a comment below and we'll take a look. If you doubt why the selected answer is correct or need additional more details? Please drop a comment or Contact us directly. Your email address will not be published. Required fields are marked *