Class 11th Physics Motion in Plane Physics

Consider a series of steps as shown. A ball is thrown from O. Find the minimum speed of directly jump to 5th step.

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mn>5</mn> <mrow> <mo>(</mo> <mrow> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mtext> </mtext> <mi>m</mi> <mo>/</mo> <mi>s</mi> </mrow> </math> </span></p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mn>5</mn> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mtext> </mtext> <mi>m</mi> <mo>/</mo> <mi>s</mi> </mrow> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mn>5</mn> <mroot> <mrow> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mo>+</mo> <mn>1</mn> </mrow> <mrow></mrow> </mroot> <mtext> </mtext> <mi>m</mi> <mo>/</mo> <mi>s</mi> </mrow> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mn>6</mn> <mroot> <mrow> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> <mo>+</mo> <mn>1</mn> </mrow> <mrow></mrow> </mroot> <mtext> </mtext> <mi>m</mi> <mo>/</mo> <mi>s</mi> </mrow> </math> </span></p>

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Alok Kumar Singh | Contributor-Level 10

4 months ago

Correct Option - 3

Detailed Solution:

$y = x t a n θ - \frac{g x^{2}}{2 v^{2} c o s^{2} θ}$

(2.5, 2.5) must lie on this

-> $1 = t a n θ - \frac{g * 2.5}{2 v^{2} c o s^{2} θ}$

-> $\frac{25}{2 v^{2} c o s^{2} θ} = t a n θ - 1$

-> $v^{2} = \frac{25}{2} {\frac{1 + t a n^{2} θ}{t a n θ - 1}}$

-> $v_{m i n} = 5 \sqrt[]{\sqrt[]{2} + 1}$

[Happens when tan θ = $\sqrt[]{2}$ + 1]

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