Class 11th Physics Physics Motion in Plane Projectile Motion

A helicopter is flying horizontally with a speed 'v' at an altitude 'h' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mroot> <mrow> <mn>2</mn> <mi>g</mi> <mi>h</mi> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mroot> <mrow> <mfrac> <mrow> <mn>2</mn> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mi>h</mi> </mrow> <mrow> <mi>g</mi> </mrow> </mfrac> <mo>+</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mroot> <mrow> <mfrac> <mrow> <mn>2</mn> <mi>g</mi> <mi>h</mi> </mrow> <mrow> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> <mo>+</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mroot> <mrow> <mfrac> <mrow> <mn>2</mn> <mi>g</mi> <mi>h</mi> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>

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Answered by

Raj Pandey | Contributor-Level 9

6 months ago

Correct Option - 2

Detailed Solution:

$h = \frac{1}{2} g t^{2}$

or $x = v \sqrt[]{\frac{2 h}{g}}$

So, x = vt

or, $x = v \frac{2 h}{g}$

So, dist of man from helicopter is

$\sqrt[]{h^{2} + x^{2}} = \sqrt[]{h^{2} + v^{2} \frac{2 h}{g}} = \sqrt[]{\frac{2 v^{2} h}{g} + h^{2}}$

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