Question

A body dropped from certain height travels 36% of total distance in the last second of its free fall. Than the time of its free fall is
1) 3.6 seconds 2) 2 seconds
3) 4 seconds 4) 5 seconds

Answer 1

A body dropped from certain height travels 36% of total distance in the last second of its free fall

Explanation :

Initial velocity , u = 0 m/s

Total time = " t " s

Let total distance be " x " m

Distance covered in t s = 36 x %

Distance travelled in ( t - 1 ) s

= ( 100 - 36 ) x %

= 64x %

= 0.64x

Apply 2nd equation of motion for total time ,

$\to \sf s=ut+\dfrac{1}{2}at^2\\\\\to \sf x=(0)t+\dfrac{gt^2}{2}\\\\\to \sf x=\dfrac{gt^2}{2}...(1)$

For ( t - 1 ) seconds ,

$\to \sf 0.64x=(0)t+\dfrac{1}{2}g(t-1)^2\\\\\to \sf 0.64x=\dfrac{g(t-1)^2}{2}...(2)$

Solve (2) ÷ (1) ,

$\to \sf \dfrac{0.64x}{x}=\dfrac{\frac{g(t-1)^2}{2}}{\frac{gt^2}{2}}\\\\\to \sf 0.64=\dfrac{(t-1)^2}{t^2}\\\\\to \sf 0.64=\left(\dfrac{t-1}{t}\right)^2\\\\\to \sf 0.8=\dfrac{t-1}{t}\\\\\to \sf 0.8t=t-1\\\\\to \sf 0.2t=1\\\\\to \sf \pink{t=5\ s}\ \; \bigstar$

So , Option (4) is correct

Answer 2

Answer:

Let the Total Distance be 100 m

Distance traveled out of free fall will be (100 - 36)% = 64% of total distance i.e. 64 m

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Let the Time taken be t

Time taken for 64 m will be (t - 1)

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Initial Velocity will be 0 m/s

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• According to the Question :

⇒ s = ut + 1/2gt²

⇒ 100 = (0 × t) + 0.5gt²

⇒ 100 = 0.5gt² ⠀⠀⠀— eq. ( I )

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• For the Rest of Distance :

⇒ s = ut + 1/2gt²

⇒ 64 = (0 × (t - 1)) + 0.5g(t - 1)²

⇒ 64 = 0.5g(t - 1)² ⠀⠀⠀— eq. ( II )

$\rule{150}{1.2}$

• Dividing eq. ( I ) by eq. ( II ) :

$:\implies\sf \dfrac{100}{64}=\dfrac{0.5gt^2}{0.5g(t-1)^2}\\\\\\:\implies\sf \dfrac{25}{16}=\dfrac{t^2}{(t-1)^2}\\\\\\:\implies\sf \dfrac{25}{16}= \bigg(\dfrac{t}{t-1} \bigg)^2\\\\\\:\implies\sf \sqrt{\dfrac{25}{16}} =\dfrac{t}{t-1}\\\\\\:\implies\sf \dfrac{5}{4} =\dfrac{t}{t-1}\\\\\\:\implies\sf 5(t - 1) = 4t\\\\\\:\implies\sf 5t - 5 = 4t\\\\\\:\implies\sf 5t - 4t = 5\\\\\\:\implies\underline{\boxed{\sf t = 5 \:seconds}}$

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$\therefore\:\underline{\textsf{The time of free fall is 4) \textbf{5 seconds}}}.$