Physics, asked by cachu7587, 1 month ago

12. A bullet strikes a uniform plank with a velocity 400 m/s and comes
out with half of that velocity. What would be the velocity of the out
coming bullet if the plank were only half thick?

Answers

Answered by nilesh102

Given data : A bullet strikes a uniform plank with a velocity 400 m/s and comes out with half of that velocity.

To find : What would be the velocity of the out coming bullet if the plank were only half thick ?

Solution : Now, according to given,

⟹ Initial velocity of bullet ( u ) = 400 m/s

Let, final velocity,

⟹ Final velocity of bullet ( v ) = ½ * u

⟹ Final velocity of bullet ( v ) = ½ * 400

⟹ Final velocity of bullet ( v ) = 200 m/s

Let, thickness of plank be ‘ s ’

Now, we use kinematical equation to find velocity of the out coming bullet.

⟹ v² = u² + 2as

Where,

Here we know that, when a moving object is losing speed constantly with time, the motions is in negative acceleration, or deceleration

Hence,

⟹ Acceleration of the bullet = - a

Now, by kinematical equation :

⟹ v² = u² + 2 * ( - a ) * s

⟹ v² - u² = - 2 * a * s

⟹ 200² - 400² = - 2 * a * s

⟹ 40000 - 160000 = - 2 * a * s

⟹ - 120000 = - 2 * a * s

⟹ 120000 = 2 * a * s

⟹ a * s = 120000/2

⟹ a * s = 60000 units

Here, we need to calculate the final velocity of the out coming bullet if the plank were only half thick, Hence,

⟹ Thickness = ½ * s = s/2

Now by kinematical equation,

⟹ v² = u² - 2 * a * s/2

⟹ v² - u² = - 2 * a * s/2

⟹ v² - 400² = - a * s

⟹ v² - 400² = - 60000

⟹ v² - 160000 = - 60000

⟹ v² = - 60000 + 160000

⟹ v² = 100000

⟹ v = √100000

⟹ v = 100√10 m/s or 316.227766 m/s

Answer : When plank in half thick then, velocity of bullet is 100√10 m/s or 316.227766 m/s .

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