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3 years ago

6

In midair an M = 145 kg bomb explodes into two pieces of m1 = 115 kg and another, respectively. Before the explosion, the bomb w

as moving at 24.0 m/s to the east. After the explosion, the velocity of the m1 = 115 kg piece is 65.0 m/s to the east. Find the velocity (in m/s) (with a proper sign) of the other piece after the explosion

1 answer:

Daniel [21]3 years ago

5 0

Answer:

$v_2=-133.17m/s$ , the minus meaning west.

Explanation:

We know that linear momentum must be conserved, so it will be the same before ( $p_i$ ) and after ( $p_f$ ) the explosion. We will take the east direction as positive.

Before the explosion we have $p_i=m_iv_i=Mv_i$ .

After the explosion we have pieces 1 and 2, so $p_f=m_1v_1+m_2v_2$ .

These equations must be vectorial but since we look at the instants before and after the explosions and the bomb fragments in only 2 pieces the problem can be simplified in one dimension with direction east-west.

Since we know momentum must be conserved we have:

$Mv_i=m_1v_1+m_2v_2$

Which means (since we want $v_2$ and $M=m_1+m_2$ ):

$v_2=\frac{Mv_i-m_1v_1}{m_2}=\frac{Mv_i-m_1v_1}{M-m_1}$

So for our values we have:

$v_2=\frac{(145kg)(24m/s)-(115kg)(65m/s)}{(145kg-115kg)}=-133.17m/s$

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Answer:

The time taken by missile's clock is $4.6\times 10^{6} s$

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As per the question:

Speed of the missile, $v_{m = 6.5\times 10^{3}} m/s$

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T' = T + 1

Now, using the time dilation eqn:

$T' = \frac{T}{\sqrt{1 + (\frac{v_{m}}{c})^{2}}}$

$\frac{T'}{T} = \frac{1}{\sqrt{1 + (\frac{v_{m}}{c})^{2}}}$

$\frac{T + 1}{T} = \frac{1}{\sqrt{1 + (\frac{v_{m}}{c})^{2}}}$

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Using binomial theorem in the above eqn:

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$(1 + x)^{a} = 1 + ax$

Thus eqn (1) becomes:

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3 years ago

car is moving at 40 m/s. At 10 meters the driver spots a deer on the road and instantly steps on the brakes. If the car is 400 k

Mice21 [21]

Answer:

32000 N

Explanation:

From the question given above, the following data were obtained:

Initial velocity (u) = 40 m/s

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Force (F) =?

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Initial velocity (u) = 40 m/s

Distance (s) = 10 m

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Acceleration (a) =?

v² = u² + 2as

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0 = 1600 + 20a

Collect like terms

0 – 1600 = 20a

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a = –1600 / 20

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The negative sign indicate that the car is decelerating i.e coming to rest.

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Answer:

Option (b) is correct.

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Inelastic collision is defined as a collision where kinetic energy of the system is not conserved whereas the linear momentum is conserved. This loss of kinetic energy may due to the conversion to thermal energy or sound energy or may be due to the deformation of the materials colliding with each other.

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