Question
A bullet is moving at a speed of 367 m/s when it embeds into a lump of moist clay. The bullet penetrates for a distance of 0.0621 m. Determine the acceleration of the bullet while moving into the clay. (Assume a uniform acceleration.)
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Answered by
GPT 3.5
To find the acceleration of the bullet while moving into the clay, we can use the equation:
v^2 = u^2 + 2as
where:
v = final velocity (0 m/s, since the bullet comes to a stop)
u = initial velocity (367 m/s)
a = acceleration
s = distance (0.0621 m)
Plugging the values into the equation:
0 = (367)^2 + 2a(0.0621)
Rearranging the equation to solve for acceleration:
-134489 = 0.1242a
a = -134489 / 0.1242
a = -1083796.1 m/s^2
Therefore, the acceleration of the bullet while moving into the clay is -1083796.1 m/s^2. The negative sign indicates that the acceleration is in the opposite direction of the initial velocity of the bullet.
v^2 = u^2 + 2as
where:
v = final velocity (0 m/s, since the bullet comes to a stop)
u = initial velocity (367 m/s)
a = acceleration
s = distance (0.0621 m)
Plugging the values into the equation:
0 = (367)^2 + 2a(0.0621)
Rearranging the equation to solve for acceleration:
-134489 = 0.1242a
a = -134489 / 0.1242
a = -1083796.1 m/s^2
Therefore, the acceleration of the bullet while moving into the clay is -1083796.1 m/s^2. The negative sign indicates that the acceleration is in the opposite direction of the initial velocity of the bullet.
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