The ans = -3.9 westward i.e the train before collision was eastward therefore after collision it goes westward ( rebounce)

Pls the example that was done on conservation of momentum , according to the question the Mass2 was onekg but it was changed to twokg in the solution

<section>
<h2>Collisions</h2>
<p>We have shown that the net change in momentum is zero for an isolated system. The momenta of the <strong>individual objects can change</strong> but the total momentum of the <strong>system remains constant</strong>.</p>
<p>This means that it makes sense to define the total momentum at the begining of the problem as the initial total momentum, $\vec{p}_{Ti}$, and the final total momentum $\vec{p}_{Tf}$. Momentum conservation implies that, no matter what happens inside an isolated system:</p>
<p>\[\vec{p}_{Ti} = \vec{p}_{Tf}\]</p>
<p>This means that in an isolated system the total momentum before a <strong>collision</strong> or <strong>explosion</strong> is equal to the total momentum after the collision or explosion.</p>
<p>Consider a simple collision of two billiard balls. The balls are rolling on a frictionless, horizontal surface and the system is isolated. We can apply conservation of momentum. The first ball has a mass ${m}_{1}$ and an initial velocity $\vec{v}_{i1}$. The second ball has a mass ${m}_{2}$ and moves first ball with an initial velocity $\vec{v}_{i2}$. This situation is shown in <a href="#attachment_109174">the figure below</a>.</p>
<p><img alt="" src="https://data.ulearngo.com/assets/fec2e233-f841-4032-8df6-d350bf2db882"/></p>
<div class="wp-caption alignnone" id="attachment_109174" style="width: 388px"><a href="https://data.ulearngo.com/assets/b934ac80-04b5-4ca2-b3dd-6aa4fd96f0c9"><img alt="" class="size-full wp-image-109174" height="93" src="https://data.ulearngo.com/assets/b934ac80-04b5-4ca2-b3dd-6aa4fd96f0c9" width="388"/></a><p class="wp-caption-text">Before the collision.</p></div>
<p>The total momentum of the system before the collision, $\vec{p}_{Ti}$ is:</p>
<p>$\vec{p}_{Ti}={m}_{1}\vec{v}_{i1}+{m}_{2}\vec{v}_{i2}$</p>
<p>After the two balls collide and move away they each have a different momentum. If the first ball has a final velocity of $\vec{v}_{f1}$ and the second ball has a final velocity of $\vec{v}_{f2}$ then we have the situation shown in the figure below.</p>
<div class="wp-caption alignnone" style="width: 388px"><img alt="e27e690a356001cd4f99609fde1b799c.png" height="93" src="https://data.ulearngo.com/assets/dd337f74-ff56-4803-937d-b03d56cfd3a3" width="388"/><p class="wp-caption-text">After the collision.</p></div>
<p>The total momentum of the system after the collision, $\vec{p}_{Tf}$ is:</p>
<p>$\vec{p}_{Tf}={m}_{1}\vec{v}_{f1}+{m}_{2}\vec{v}_{f2}$</p>
<p>This system of two balls is isolated since there are no external forces acting on the balls. Therefore, by the principle of conservation of linear momentum, the total momentum before the collision is equal to the total momentum after the collision. This gives the equation for the conservation of momentum in a collision of two objects,</p>
<table>
<tbody>
<tr>
<td colspan="2">
<p>$\vec{p}_{i}=\vec{p}_{f}$</p>
</td>
</tr>
<tr>
<td colspan="2">
<p>${m}_{1}\vec{v}_{i1}+{m}_{2}\vec{v}_{i2}={m}_{1}\vec{v}_{f1}+{m}_{2}\vec{v}_{f2}$</p>
</td>
</tr>
<tr>
<td>
<p>${m}_{1}$</p>
</td>
<td>
<p>: mass of object 1 (kg)</p>
</td>
</tr>
<tr>
<td>
<p>${m}_{2}$</p>
</td>
<td>
<p>: mass of object 2 (kg)</p>
</td>
</tr>
<tr>
<td>
<p>$\vec{v}_{i1}$</p>
</td>
<td>
<p>: initial velocity of object 1 ($\text{m·s$^{-1}$}$ + direction)</p>
</td>
</tr>
<tr>
<td>
<p>$\vec{v}_{i2}$</p>
</td>
<td>
<p>: initial velocity of object 2 ($\text{m·s$^{-1}$}$ - direction)</p>
</td>
</tr>
<tr>
<td>
<p>$\vec{v}_{f1}$</p>
</td>
<td>
<p>: final velocity of object 1 ($\text{m·s$^{-1}$}$ - direction)</p>
</td>
</tr>
<tr>
<td>
<p>$\vec{v}_{f2}$</p>
</td>
<td>
<p>: final velocity of object 2 ($\text{m·s$^{-1}$}$ + direction)</p>
</td>
</tr>
</tbody>
</table>
<p>This equation is always true - momentum is always conserved in collisions.</p>
<div class="ns-school-emp">
<h2>Example: Conservation of Momentum</h2>
<div class="ns-school-defn">
<h3>Question</h3>
<div>
<p>A toy car of mass $\text{1}$ $\text{kg}$ moves westwards with a speed of $\text{2}$ $\text{m·s$^{-1}$}$. It collides head-on with a toy train. The train has a mass of $\text{1.5}$ $\text{kg}$ and is moving at a speed of $\text{1.5}$ $\text{m·s$^{-1}$}$ eastwards. If the car rebounds at $\text{2.05}$ $\text{m·s$^{-1}$}$, calculate the final velocity of the train.</p>
<h3>Solution</h3>
</div>
<div>
<h3>Step 1: Analyse what you are given and draw a sketch</h3>
<p>The question explicitly gives a number of values which we identify and convert into SI units if necessary:</p>
<ul>
<li>
<p>the train's mass (${m}_{1}= \text{1.50}\text{ kg}$),</p>
</li>
<li>
<p>the train's initial velocity ($\vec{v}_{1i}=\text{1.5}\text{ m·s$^{-1}$}$ eastward),</p>
</li>
<li>
<p>the car's mass (${m}_{2}= \text{1.00}\text{ kg}$),</p>
</li>
<li>
<p>the car's initial velocity ($\vec{v}_{2i}=\text{2.00}\text{ m·s$^{-1}$}$ westward), and</p>
</li>
<li>
<p>the car's final velocity ($\vec{v}_{2f}=\text{2.05}\text{ m·s$^{-1}$}$ eastward).</p>
</li>
</ul>
<p>We are asked to find the final velocity of the train.</p>
<img alt="331e1f16a76c7f7e74adb981dfbeae6e.png" src="https://data.ulearngo.com/assets/1fd4db20-c198-4a64-88f0-c83a798de735"/></div>
<div>
<h3>Step 2: Choose a frame of reference</h3>
<p>We will choose to the East as positive.</p>
</div>
<div>
<h3>Step 3: Apply the Law of Conservation of momentum</h3>

\begin{align*} \vec{p}_{Ti}&amp; = \vec{p}_{Tf} \\ {m}_{1}\vec{v}_{i1}+{m}_{2}\vec{v}_{i2}&amp; = {m}_{1}\vec{v}_{f1}+{m}_{2}\vec{v}_{f2} \\ \left(\text{1.5}\right)\left(\text{+1.5} \right)+\left(2\right)\left(-2 \right)&amp; = \left(\text{1.5}\right)\left(\vec{v}_{f1}\right)+\left(2\right)\left(\text{2.05} \right) \\ \text{2.25} -4 -\text{4.1}&amp; = \left(\text{1.5}\right)\vec{v}_{f1} \\ \text{5.85} &amp; = \left(\text{1.5}\right)\vec{v}_{f1} \\ \vec{v}_{f1}&amp; = \text{3.9} \text{m}·{\text{s}}^{-1} \text{eastwards}\end{align*}</div>
</div>
</div>
</section>
<section></section>

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Collisions

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Collisions

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