Question

(d) jono releases his \\(10\text{ kg}\\) dog and it runs directly towards the neighbours dog at \\(1.1\text{ m s}^{-1}\\). the neighbours dog, mass \\(12\text{ kg}\\), runs directly towards jonos dog. they collide, stick together, and slide across the floor at \\(0.30\text{ m s}^{-1}\\).

calculate the speed that the neighbours dog was moving at before the collision.

Explanation:

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<reasoning>

Identify given parameters

We define the system parameters from the problem statement:

• Mass of Jono's dog, \(m_1 = 10\text{ kg}\)
• Initial velocity of Jono's dog, \(u_1 = -1.1\text{ m s}^{-1}\) (moving left)
• Mass of the neighbour's dog, \(m_2 = 12\text{ kg}\)
• Initial velocity of the neighbour's dog, \(u_2 = v\) (moving right)
• Combined mass after collision, \(m_1 + m_2 = 22\text{ kg}\)
• Final velocity after collision, \(v_f = 0.30\text{ m s}^{-1}\) (moving right)

Set up momentum equation

Using the Conservation of Momentum principle:
\[
m_1 u_1 + m_2 u_2 = (m_1 + m_2) v_f
\]

Substitute known values

Substitute the values into the conservation equation:
\[
(10\text{ kg})(-1.1\text{ m s}^{-1}) + (12\text{ kg})(v) = (10\text{ kg} + 12\text{ kg})(0.30\text{ m s}^{-1})
\]
\[
-11 + 12v = 22 \times 0.30
\]

Solve for the unknown velocity

Simplify and solve for \(v\):
\[
-11 + 12v = 6.6
\]
\[
12v = 17.6
\]
\[
v = \frac{17.6}{12} \approx 1.47\text{ m s}^{-1}
\]
</reasoning>

<answer>
\(1.5\text{ m s}^{-1}\) (or \(1.47\text{ m s}^{-1}\))
</answer>

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Answer:

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<reasoning>

Identify given parameters

We define the system parameters from the problem statement:

• Mass of Jono's dog, \(m_1 = 10\text{ kg}\)
• Initial velocity of Jono's dog, \(u_1 = -1.1\text{ m s}^{-1}\) (moving left)
• Mass of the neighbour's dog, \(m_2 = 12\text{ kg}\)
• Initial velocity of the neighbour's dog, \(u_2 = v\) (moving right)
• Combined mass after collision, \(m_1 + m_2 = 22\text{ kg}\)
• Final velocity after collision, \(v_f = 0.30\text{ m s}^{-1}\) (moving right)

Set up momentum equation

Using the Conservation of Momentum principle:
\[
m_1 u_1 + m_2 u_2 = (m_1 + m_2) v_f
\]

Substitute known values

Substitute the values into the conservation equation:
\[
(10\text{ kg})(-1.1\text{ m s}^{-1}) + (12\text{ kg})(v) = (10\text{ kg} + 12\text{ kg})(0.30\text{ m s}^{-1})
\]
\[
-11 + 12v = 22 \times 0.30
\]

Solve for the unknown velocity

Simplify and solve for \(v\):
\[
-11 + 12v = 6.6
\]
\[
12v = 17.6
\]
\[
v = \frac{17.6}{12} \approx 1.47\text{ m s}^{-1}
\]
</reasoning>

<answer>
\(1.5\text{ m s}^{-1}\) (or \(1.47\text{ m s}^{-1}\))
</answer>

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