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2 years ago

8

A 1250-kg compact car is moving with velocity v1 =36.2i^+12.7j^m/s. It skids on a frictionless icy patch and collides with a 448

-kg hay wagon moving with velocity v2=13.8i^+10.2j^m/s.
If the two stay together, what is their velocity?
Express your answer in meters per second in terms of i^ and j^. Use the 'unit vector' button to denote unit vectors in your answer.

1 answer:

MA_775_DIABLO [31]2 years ago

7 0

Momentum is conserved, so the sum of the separate momenta of the car and wagon is equal to the momentum of the combined system:

(1250 kg) ((36.2 <em>i</em> + 12.7 <em>j </em>) m/s) + (448 kg) ((13.8 <em>i</em> + 10.2 <em>j</em> ) m/s) = ((1250 + 448) kg) <em>v</em>

where <em>v</em> is the velocity of the system. Solve for <em>v</em> :

<em>v</em> = ((1250 kg) ((36.2 <em>i</em> + 12.7 <em>j </em>) m/s) + (448 kg) ((13.8 <em>i</em> + 10.2 <em>j</em> ) m/s)) / (1698 kg)

<em>v</em> ≈ (30.3 <em>i</em> + 12.0 <em>j</em> ) m/s

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Answer:

1.1 m/s²

Explanation:

From the question,

F -mgμ = ma.................... Equation 1

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Given: F = 115 N, m = 25 kg, μ = 0.35

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Substitute these values into equation 2

115-(25×10×0.35) = 25×a

115-87.5 = 25a

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Answer:

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Explanation:

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attached below is the remaining part of the solution

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The opening to a cave is a tall, 30.0-cm-wide crack. A bat is preparing to leave the cave emits a 30.0 kHz ultrasonic chirp. How

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Answer:

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Explanation:

From the question we are told that

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=> $\lambda = \frac{340 }{30*10^{3}}$

=> $\lambda = 0.0113 \ m/s$

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=> $y = \frac{ 1 * 0.0113 * 100}{0.3}$

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Answer:

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$Q_1=mL_s\\\Rightarrow Q_1=m(2.256\times 10^6)$

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$Q_2=ms_w\Delta T\\\Rightarrow Q_2=m4186\times (100-0)\\\Rightarrow Q_2=m0.4186\times 10^6$

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Total heat released is

$Q=Q_1+Q_2+Q_3\\\Rightarrow Q=m(2.256\times 10^6)+m0.4186\times 10^6+m(0.3335\times 10^6)\\\Rightarrow Q=3008100m$

The kinetic energy of the bullet will balance the heat

$K=Q\\\Rightarrow \frac{1}{2}mv^2=3008100m\\\Rightarrow v=\sqrt{2\times 3008100}\\\Rightarrow v=2452.79432\ m/s$

The velocity of the ice would be 2452.79432 m/s

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