Two bodies begin a free fall from rest, from the same height, 1 second apart. How long after the first body begins to fall, will the two bodies be 10 m apart? (1) 25 (2) 3.5 s (3) 0.5 s [(4) 1.5 S

Answers 1

Answer:

The required time lapse is (4) 1.5 s.

Explanation:

Let , the first body fell 's' meters down in 't' seconds.

According to the question , the second body fell 's₀' meters in ( t - 1 ) seconds.

Both of them started falling from rest , so the initial velocity for both body is 0 m/s .

let , the acceleration due to gravity is g = 10 m/s²

then , s = 0 × t + ( 1/2)gt² ⇒ s = (1/2)gt²

and , s₀ = 0 × t + ( 1/2 )g( t - 1 )² ⇒ s₀ = ( 1/2 )g( t - 1 )²

According to the question ,

s₀ = s - 10

⇒ ( 1/2 )g( t - 1 )² = (1/2)gt² - 10

⇒ ( 1/2 )g( t² - 2t + 1 ) = (1/2)gt² - 10

⇒ ( 1/2 )gt² - gt + g/2 = (1/2)gt² - 10

⇒ gt = 10 + g/2

⇒ 10t = 10 + 5

⇒ 10t = 15

⇒ t = 1.5 seconds