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