A student fixes two ends of a rope to two rigid supports A and B, placed at a distance of 15m. He then gives a transverse horizontal jerk to create a pulse in the rope which moves from A to B, B to A, repeatedly. The pulse dies after completing three, to and fro journeys from A to B and back. The pulse takes 2 min and 30s to complete its entire journey. The speed of the pulse moving on the rope is
Question
A student fixes two ends of a rope to two rigid supports A and B, placed at a distance of 15m. He then gives a transverse horizontal jerk to create a pulse in the rope which moves from A to B, B to A, repeatedly. The pulse dies after completing three, to and fro journeys from A to B and back. The pulse takes 2 min and 30s to complete its entire journey. The speed of the pulse moving on the rope is
Solution
To find the speed of the pulse moving on the rope, we can use the formula:
Speed = Distance / Time
First, let's calculate the total distance traveled by the pulse. The pulse completes three to and fro journeys from A to B and back. Since the distance between A and B is 15m, the total distance traveled by the pulse is:
Total Distance = 3 journeys * 2 distances * 15m = 90m
Next, let's convert the given time of 2 minutes and 30 seconds into seconds:
Time = 2 minutes * 60 seconds/minute + 30 seconds = 120 seconds + 30 seconds = 150 seconds
Now, we can calculate the speed of the pulse:
Speed = Total Distance / Time = 90m / 150s = 0.6 m/s
Therefore, the speed of the pulse moving on the rope is 0.6 m/s.
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