Question

a bullet on penetrating two successive wooden planks of unequal thickness loses its velocity by 200ms^-1in each case.if the initial velocity of the bullet is 1000 m.s^-1, calculate the ratio of thickness of the planks.

Answer 1

$\bf \underline{Question}$

A bullet on penetrating two successive wooden planks of unequal thickness loses its velocity by 200 m/s in each case. If the initial velocity of the bullet is 1000 m/s , Calculate the ratio of thickness of the planks.

$\pink{\huge \frak{Answer}}$

$\colorbox{pink}{9 : 7}$

Solution

Given that ,

• Loss of Velocity = 200 m/s
• Initial Velocity of bullet = 1000 m/s

After penetrating first block , Final velocity is

$\footnotesize \: v_f = 1000 - 200 = \bf \blue{800 \: ms ^{ - 1}}$

For the second block ,

$\sf \:v_I = 800 \: m/s$

and , Final Velocity would be

$\footnotesize v_f = 800 - 200 = \bf \blue{600 ms^{ - 1}}$

Thickness of the first Block

Using third equation of motion

$\boxed{\rm\boxed{v ^{2} - {u}^{2} = 2as}} \red\bigstar$

$: \implies \rm 1000 ^{2} - 800^{2} = 2as \\ \rm as \: = \red{18000 \: m {s}^{ - 1}} \longrightarrow(1)$

Thickness of the second Block

Using third equation of motion

$\boxed{\rm\boxed{v ^{2} - {u}^{2} = 2as'}} \pink\bigstar$

$: \implies \rm 800 ^{2} - 600^{2} = 2as' \\ \rm as' \: = \red{14000 \: m {s'}^{ - 1}} \longrightarrow(2)$

To Find

The ratio of thickness of planks , i.e.

$\bf \dfrac{as}{as'} = \dfrac{ 18\cancel{000}}{ 14\cancel{000}} = \dfrac{9}{4}$

Conclusion

9 : 4 is the required ratio for the thickness of planks.

$\huge\frak{ \orange{Thankyou}}$