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A police inspector in a jeep is chasing a pickpocket on a straight road. The jeep is going at its maximum speed v (assumed uniform). The pickpocket rides on the motorcycle of a waiting friend when the jeep is at a distance d away, and the motorcycle starts with a constant acceleration a. Show that the pick pocket will be caught if v≥ √2ad.?
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A police inspector in a jeep is chasing a pickpocket on a straight roa...
Analysis:
To determine if the pickpocket will be caught, we need to consider the relative speeds of the jeep and the motorcycle.
Distance covered by the jeep:
The jeep covers a distance d at speed v before the pickpocket starts riding the motorcycle.
Distance covered by the motorcycle:
Let t be the time taken for the motorcycle to catch up to the jeep. The distance covered by the motorcycle during this time is given by:
\[d = \frac{1}{2}at^2\]
Equating the distances:
Setting the two distances equal to each other, we have:
\[d = \frac{1}{2}at^2\]
\[d = vt\]
Solving for t, we get:
\[t = \frac{2d}{v}\]
Condition for the pickpocket to be caught:
For the pickpocket to be caught, the time taken for the motorcycle to catch up to the jeep should be less than the time it would take for the jeep to cover the same distance. In other words:
\[t < />
Substituting the expression for t, we get:
\[\frac{2d}{v} < />
\[2 < />
This inequality is not true, which means that the pickpocket will not be caught if \(v < />
Conclusion:
Therefore, the pickpocket will be caught if and only if \(v \geq \sqrt{2ad}\).
To determine if the pickpocket will be caught, we need to consider the relative speeds of the jeep and the motorcycle.
Distance covered by the jeep:
The jeep covers a distance d at speed v before the pickpocket starts riding the motorcycle.
Distance covered by the motorcycle:
Let t be the time taken for the motorcycle to catch up to the jeep. The distance covered by the motorcycle during this time is given by:
\[d = \frac{1}{2}at^2\]
Equating the distances:
Setting the two distances equal to each other, we have:
\[d = \frac{1}{2}at^2\]
\[d = vt\]
Solving for t, we get:
\[t = \frac{2d}{v}\]
Condition for the pickpocket to be caught:
For the pickpocket to be caught, the time taken for the motorcycle to catch up to the jeep should be less than the time it would take for the jeep to cover the same distance. In other words:
\[t < />
Substituting the expression for t, we get:
\[\frac{2d}{v} < />
\[2 < />
This inequality is not true, which means that the pickpocket will not be caught if \(v < />
Conclusion:
Therefore, the pickpocket will be caught if and only if \(v \geq \sqrt{2ad}\).
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A police inspector in a jeep is chasing a pickpocket on a straight road. The jeep is going at its maximum speed v (assumed uniform). The pickpocket rides on the motorcycle of a waiting friend when the jeep is at a distance d away, and the motorcycle starts with a constant acceleration a. Show that the pick pocket will be caught if v≥ √2ad.?
Question Description
A police inspector in a jeep is chasing a pickpocket on a straight road. The jeep is going at its maximum speed v (assumed uniform). The pickpocket rides on the motorcycle of a waiting friend when the jeep is at a distance d away, and the motorcycle starts with a constant acceleration a. Show that the pick pocket will be caught if v≥ √2ad.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A police inspector in a jeep is chasing a pickpocket on a straight road. The jeep is going at its maximum speed v (assumed uniform). The pickpocket rides on the motorcycle of a waiting friend when the jeep is at a distance d away, and the motorcycle starts with a constant acceleration a. Show that the pick pocket will be caught if v≥ √2ad.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A police inspector in a jeep is chasing a pickpocket on a straight road. The jeep is going at its maximum speed v (assumed uniform). The pickpocket rides on the motorcycle of a waiting friend when the jeep is at a distance d away, and the motorcycle starts with a constant acceleration a. Show that the pick pocket will be caught if v≥ √2ad.?.
A police inspector in a jeep is chasing a pickpocket on a straight road. The jeep is going at its maximum speed v (assumed uniform). The pickpocket rides on the motorcycle of a waiting friend when the jeep is at a distance d away, and the motorcycle starts with a constant acceleration a. Show that the pick pocket will be caught if v≥ √2ad.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A police inspector in a jeep is chasing a pickpocket on a straight road. The jeep is going at its maximum speed v (assumed uniform). The pickpocket rides on the motorcycle of a waiting friend when the jeep is at a distance d away, and the motorcycle starts with a constant acceleration a. Show that the pick pocket will be caught if v≥ √2ad.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A police inspector in a jeep is chasing a pickpocket on a straight road. The jeep is going at its maximum speed v (assumed uniform). The pickpocket rides on the motorcycle of a waiting friend when the jeep is at a distance d away, and the motorcycle starts with a constant acceleration a. Show that the pick pocket will be caught if v≥ √2ad.?.
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