A police party is chasing a dacoit in a jeep which is moving at a constant speed \(v .\) The dacoit is on a…
A police party is chasing a dacoit in a jeep which is moving at a constant speed \(v .\) The dacoit is on a motor cycle. When he is at a distance \(x\) from the jeep he accelerates from rest at a constant rate. Which of the following relations is true, if the police is able to catch the dacoit?
\(v^{2} \leq \alpha x\)
\(v^{2} \leq 2 \alpha x\)
\(v^{2} \geq 2 \alpha x\)
\(v^{2} \geq \alpha x\)
Solution
If police is able to catch the dacoit after time \(t\), then \(v t \geq x+\frac{1}{2} \alpha t^{2} .\) This gives \(\frac{\alpha}{2} t^{2}-v t+x=0\)
or \(t=\frac{v \pm \sqrt{v^{2}-2 \alpha x}}{\alpha}\)
For \(t\) to be real, \(v^{2} \geq 2 \alpha x\)
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Asked in: JEE Mains - Motion In One Dimension - Chapter Test