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A bullet fired into a fixed wooden block loses half of its velocity after penetrating 40cm. It comes to rest after penetrating a further distance of
- a)22/3 cm
- b)40/3 cm
- c)20/3 cm
- d)22/5 cm
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A bullet fired into a fixed wooden block loses half of its velocity af...
For first part of penetration, by equation of motion
For later part of penetration
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Community Answer
A bullet fired into a fixed wooden block loses half of its velocity af...
Given data:
Initial velocity of bullet (u) = ?
Final velocity of bullet (v) = 0
Distance travelled by bullet after losing half of its velocity = 40 cm
Total distance travelled by bullet before coming to rest = ?
Using the formula of velocity after displacement:
v^2 = u^2 + 2as
where,
v = final velocity (0 m/s)
u = initial velocity
a = acceleration (deceleration in this case)
s = displacement
After penetrating 40 cm, the velocity of bullet becomes half of the initial velocity i.e. u/2. Therefore,
v^2 = (u/2)^2 + 2a(40 cm)
Simplifying the above equation, we get:
a = -u^2/3200 m/s^2 (negative sign indicates deceleration)
Now, using the same formula of velocity after displacement for the remaining distance travelled by bullet:
v^2 = u^2 + 2as
Putting the values of v, a and s, we get:
0 = u^2 + 2(-u^2/3200)(20/3)
Simplifying the above equation, we get:
u = 40/3 m/s
Finally, using the same formula of velocity after displacement for the total distance travelled by bullet:
v^2 = u^2 + 2as
Putting the values of v, u and a, we get:
0 = (40/3)^2 + 2(-u^2/3200)s
Simplifying the above equation and solving for s, we get:
s = 40/3 cm
Therefore, the correct answer is option B, i.e. 40/3 cm.
Initial velocity of bullet (u) = ?
Final velocity of bullet (v) = 0
Distance travelled by bullet after losing half of its velocity = 40 cm
Total distance travelled by bullet before coming to rest = ?
Using the formula of velocity after displacement:
v^2 = u^2 + 2as
where,
v = final velocity (0 m/s)
u = initial velocity
a = acceleration (deceleration in this case)
s = displacement
After penetrating 40 cm, the velocity of bullet becomes half of the initial velocity i.e. u/2. Therefore,
v^2 = (u/2)^2 + 2a(40 cm)
Simplifying the above equation, we get:
a = -u^2/3200 m/s^2 (negative sign indicates deceleration)
Now, using the same formula of velocity after displacement for the remaining distance travelled by bullet:
v^2 = u^2 + 2as
Putting the values of v, a and s, we get:
0 = u^2 + 2(-u^2/3200)(20/3)
Simplifying the above equation, we get:
u = 40/3 m/s
Finally, using the same formula of velocity after displacement for the total distance travelled by bullet:
v^2 = u^2 + 2as
Putting the values of v, u and a, we get:
0 = (40/3)^2 + 2(-u^2/3200)s
Simplifying the above equation and solving for s, we get:
s = 40/3 cm
Therefore, the correct answer is option B, i.e. 40/3 cm.
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Question Description
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