A football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is:

Correct Option - 4


Detailed Solution:

Initial velocity $=-v\hat{j}$

Final velocity $=-v\hat{j}$  

Change in velocity $=v\hat{i}-(-v\hat{j})$

$=v(\hat{i}+\hat{j})$ Momentum gain is along $\stackrel{\mathrm{ˆ}}{\mathrm{i}}+\stackrel{\mathrm{ˆ}}{\mathrm{j}}$

$\Rightarrow$ Force experienced is along $\stackrel{\mathrm{ˆ}}{\mathrm{i}}+\stackrel{\mathrm{ˆ}}{\mathrm{j}}$

$\Rightarrow$ Force experienced is in North-East direction.

<p>Initial velocity <span contenteditable="false"> <math> <mo>=</mo> <mo>-</mo> <mi>v</mi> <mover accent="true"> <mrow> <mrow> <mi>j</mi> </mrow> </mrow> <mi>ˆ</mi> </mover> </math> </span>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p><p>Final velocity <span contenteditable="false"> <math> <mo>=</mo> <mo>-</mo> <mi>v</mi> <mover accent="true"> <mrow> <mrow> <mi>j</mi> </mrow> </mrow> <mi>ˆ</mi> </mover> </math> </span>&nbsp;</p><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1757044026phpjOvKsF.jpeg" alt="" width="116" height="79" loading="lazy"></picture></div></div><p>Change in velocity <span contenteditable="false"> <math> <mo>=</mo> <mi>v</mi> <mover accent="true"> <mrow> <mrow> <mi>i</mi> </mrow> </mrow> <mi>ˆ</mi> </mover> <mo>-</mo> <mo> (</mo> <mo>-</mo> <mi>v</mi> <mover accent="true"> <mrow> <mrow> <mi>j</mi> </mrow> </mrow> <mi>ˆ</mi> </mover> <mo>)</mo> </math> </span>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p><p><span contenteditable="false"> <math> <mo>=</mo> <mi>v</mi> <mo> (</mo> <mover accent="true"> <mrow> <mrow> <mi>i</mi> </mrow> </mrow> <mi>ˆ</mi> </mover> <mo>+</mo> <mover accent="true"> <mrow> <mrow> <mi>j</mi> </mrow> </mrow> <mi>ˆ</mi> </mover> <mo>)</mo> </math> </span>Momentum gain is along <span contenteditable="false"> <math> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">i</mi> </mrow> </mrow> <mi mathvariant="normal">ˆ</mi> </mover> <mo>+</mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">j</mi> </mrow> </mrow> <mi mathvariant="normal">ˆ</mi> </mover> </math> </span>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p><p><span contenteditable="false"> <math> <mo>⇒</mo> </math> </span> Force experienced is along <span contenteditable="false"> <math> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">i</mi> </mrow> </mrow> <mi mathvariant="normal">ˆ</mi> </mover> <mo>+</mo> <mover accent="true"> <mrow> <mrow> <mi mathvariant="normal">j</mi> </mrow> </mrow> <mi mathvariant="normal">ˆ</mi> </mover> </math> </span>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p><p><span contenteditable="false"> <math> <mo>⇒</mo> </math> </span> Force experienced is in North-East direction.</p><p>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p><p>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p>

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