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A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest, assuming that it faces constant resistance to motion?
- a)1 cm
- b)2 cm
- c)3 cm
- d)4 cm
Correct answer is option 'A'. Can you explain this answer?
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A bullet fired into a fixed target loses half of its velocity after pe...
Given, the bullet loses half of its velocity after penetrating 3 cm.
Let the initial velocity of the bullet be 'u' and final velocity be 'v'.
Using the formula, v^2 - u^2 = 2as, where 's' is the distance travelled, we get:
(v/2)^2 - u^2 = 2a*3
Simplifying, we get:
(v/2 + u)(v/2 - u) = 6a
Since the bullet comes to rest, final velocity v = 0.
Thus, we have:
(u/2)(-u/2) = 6a
Simplifying further:
u^2 = -24a
We know that the resistance to motion is constant, which implies that the acceleration 'a' is also constant.
Let the distance travelled by the bullet before coming to rest be 'd'.
Using the formula, v^2 - u^2 = 2as, we get:
0 - u^2 = 2ad
Substituting the value of 'a' from the earlier equation, we get:
u^2 = -24a = -24(-u^2/2d)
Simplifying, we get:
d = 1 cm
Therefore, the bullet will penetrate 1 cm further before coming to rest.
Hence, option 'A' is the correct answer.
Let the initial velocity of the bullet be 'u' and final velocity be 'v'.
Using the formula, v^2 - u^2 = 2as, where 's' is the distance travelled, we get:
(v/2)^2 - u^2 = 2a*3
Simplifying, we get:
(v/2 + u)(v/2 - u) = 6a
Since the bullet comes to rest, final velocity v = 0.
Thus, we have:
(u/2)(-u/2) = 6a
Simplifying further:
u^2 = -24a
We know that the resistance to motion is constant, which implies that the acceleration 'a' is also constant.
Let the distance travelled by the bullet before coming to rest be 'd'.
Using the formula, v^2 - u^2 = 2as, we get:
0 - u^2 = 2ad
Substituting the value of 'a' from the earlier equation, we get:
u^2 = -24a = -24(-u^2/2d)
Simplifying, we get:
d = 1 cm
Therefore, the bullet will penetrate 1 cm further before coming to rest.
Hence, option 'A' is the correct answer.
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A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest, assuming that it faces constant resistance to motion?a)1 cmb)2 cmc)3 cmd)4 cmCorrect answer is option 'A'. Can you explain this answer?
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