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When a ball is allowed to fall, the time it takes to fall any distance varies as the square root of the distance and it takes 4 seconds to fall 78.40 m. How long would it take to fall 122.50 m?

When a ball is allowed to fall, the time it takes to fall any distance varies as the square root of the distance and it takes 4 seconds to fall 78.40 m. How long would it take to fall 122.50 m? Correct Answer 5 seconds

Given:

Time α √Distance

Time required to cover 78.4-meter distance = 4 s

Concept used:

If time varies as the square root of the distance, then (t12/t22) = d1/d2.

Where, t1 and t2 is the time taken whereas d1 and d2 is the distance.

Calculation:

We know that,

(t12/t22) = d1/d2

⇒ 42/t22 = 78.4/122.5

⇒ t22 = (122.5/78.4) × 16

⇒ t2 = √25

⇒ t2 = 5

∴ The required time is 5 seconds.

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