Question

A bullet of mass 10gram travelling horizontally with a velocity 150 m/s ,strikes a stationary wooden block and comes to rest in 0.03 second. Calculate the distance of penetration of the bullet into the block. Also calculate the magnitude of the force of the force exerted by the wooden block on the bullet.​

Answer 1

Answer :-

• Distance of penetration of the bullet into the block is 2.25 metres .

• Force exerted by the wooden block on the bullet is a retarding force of 50 Newtons .

Explanation :-

We have :-

→ Mass of the bullet (m) = 10 g = 0.01 kg

→ Initial velocity (u) = 150 m/s

→ Time taken (t) = 0.03 s

→ Final velocity (v) = 0

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Firstly, let's calculate acceleration of the bullet by using the 1st equation of motion .

v = u + at

⇒ 0 = 150 + (a)0.03

⇒ -150 = 0.03a

⇒ a = -150/0.03

⇒ a = -5000 m/s²

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Now, we can calculate distance of penetration of the bullet into the block by using the 3rd equation of motion.

v² - u² = 2as

⇒ 0 - (150)² = 2(-5000)(s)

⇒ -22500 = -10000s

⇒ s = -22500/-10000

⇒ s = 2.25 m

Finally, we will calculate the required force by using Newton's 2nd law of motion .

F = ma

⇒ F = 0.01(-5000)

⇒ F = -50 N

[Here, -ve sign represents retarding force] .

Answer 2

Answer:

• 2.25m.
• 50N.

Explanation:

Given:

A bullet of mass 10g travelling horizontally with a velocity 150m/s, strikes a stationary wooden block and comes to rest in 0.02s.

To find:

Distance of penetration of the bullet into the block.

Magnitude of force exerted by the wooden block on the bullet.

Solution:

We have,

› Mass (m) = 10g = 10/1000 = 0.01Kg

› Initial velocity (u) = 150m/s

› Final velocity (v) = 0m/s

› Time taken (t) = 0.03s

Finding the acceleration of the bullet,

• v = u + at

› 0 = 150 + a(0.03)

› 0 = 150 + 0.03a

› 0 - 150 = 0.03a

› -150 = 0.03a

› a = -150/0.03

∴ a = -5000 m/s²

• [Hence the body is retarding, negative acceleration]

Finding the distance of penetration of the bullet into the block,

• v² - u² = 2as

› 0² - 150² = 2(-5000)(s)

› 0 - 22500 = -10000s

› - 22500 = -10000s

› s = -22500/-10000

∴ s = 2.25 m

Finding the force exerted by the wooden block on the bullet,

• F = ma

› F = 0.01(-5000)

∴ F = -50N

• [Hence the body has retarding force]