Question:
A ship moves with a speed of 5 m/sec due east; and then it turns trough 90 degree due north and cover the same distance with speed of 7 m/sec. Calculate its average speed.
Answer:
In the problem, you need to look carefully to check if average speed is asked or average velocity is asked.
Average speed = Total path length / Total time taken
Total path length = x + x = 2x
Total time = x/5 + x/7 = 12x/35
Average speed = 2x / 12x/35 = 35/6 m/s
However, if average velocity is asked, we need to draw a vector diagram as given below and proceed further:
The average velocity is given by Total displacement /Total time taken
Total displacement = (AC) = √(AB)2 +(BC)2 = √x2 + x2 = x√2
Total time for AB = Distance/ Speed = x/5 sec
Total time for BC = Distance / Speed = x/7 sec
Total time = x/5 + x/7 = 12x/35
Average velocity = x√2 / 12x/35 = 35√2 / 12 m/s
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