Question

The seconds hand of a wall clock is 7cm long. What is the ratio of the distance to magnitude of the displacement of its tip in 15 seconds.​

Answer 1

Answer:

Unclear

Explanation:

Answer 2

Let the wall be a circle whose results is 7 cm (seconds hand)
In 15 seconds it covers an angle of 90° = 1/4 of the circle
Total distance(length) of the circle = 2πr

Thus, distance= 1/4 × 2πr = 1/2×πr
= 1/2 × 22/7 × 7= 11 cm

Displacment = shortest possible distance from the initial to the final point

Thus, If you could visualize then displacement is the line joining the starting point to the point where 90° of the clock is. {I hope you could visualise it}

Now, we join the initial point and the final point to the centre of the circle and that will be its radius = 7cm. This has resulted in the formation of a right angled triangle where two sides are 7 cm(radius) and the hypotenuse is the displacment that we have to find.

Applying Pythagoras theorem, we get hypotenuse = 7√2 cm
Hence, displacement = 7√2 cm


therefore, ratio of distance to magnitude is 11/7√2 = 11: 7√2
or you can rationalise it as follows
=11×7√2 / 98 = 11√2 / 14 = 11√2 : 14

Hope it helps,
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