Question

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Answer 1

Answer:

Hola

Explanation:

Assume that the material of the wooden block provides uniform retardation to the penetrating body at all times . This assumption is extremely important for solving this problem .

Key equation for solving this problem :

v² = u² + 2×a×s

v = velocity of the body at any later instant

u = initial velocity of the body

a = uniform acceleration ( or retardation ) of the body penetrating the wooden block

When body penetrates 3 cm into the block ,

v = u/2

a = keep it as it is

s = x = 3 cm , but keep it as ‘x’ as for now , we will plug-in the value later .

So

(u/2)² = u² - 2×a×x

Or

3u²/4 = 2×a×x —— ( 1 )

Now ,

Let the body penetrate a distance of y into the block before coming to rest .. Note that y is measured from the point where the body starts to penetrate the block … In other words , we start measuring y when the body just starts to penetrate the wooden block .

So

0² = u² - 2×a×y

Or

u² = 2×a×y —— ( 2 )

dividing equation ( 1 ) by ( 2 ) , we get

x / y = 3 / 4

Or

y = (4/3)×x

here x = 3 cm

So y = 4 cm

Hence the body penetrates an additional distance of y - x = ( 4 - 3 ) cm = 1 cm into the wooden block before coming to rest .

Hope this answer helps!