Question

A plane moving with velocity 'v' turns by theta angle and it's speed remains'v'. Find the change in velocity of plane. PLS draw the diagram and full explanation. pls its urgent

Answer 1

Given:

A plane moving with velocity 'v' turns by theta angle and it's speed remains 'v'.

To find:

Change in Velocity?

Calculation:

First of all, refer to attached diagram to understand the vectors.

• Change in velocity can be calculated as the vector difference between final and initial vector.

$\sf \: \Delta v = \sqrt{ {v}^{2} + {v}^{2} + 2.v.v \cos( {180}^{ \circ} - \theta) }$

$\sf \implies\: \Delta v = \sqrt{ {v}^{2} + {v}^{2} - 2.v.v \cos( \theta) }$

$\sf \implies\: \Delta v = \sqrt{ 2{v}^{2} - 2 {v}^{2} \cos( \theta) }$

$\sf \implies\: \Delta v = \sqrt{ 2{v}^{2} \{1 - \cos( \theta) \} }$

$\sf \implies\: \Delta v = \sqrt{ 2{v}^{2} \times 2 { \sin}^{2} \bigg( \dfrac{ \theta}{2} \bigg)}$

$\sf \implies\: \Delta v = \sqrt{4 {v}^{2} { \sin}^{2} \bigg( \dfrac{ \theta}{2} \bigg)}$

$\boxed{ \sf \implies\: \Delta v = 2 v\sin \bigg( \dfrac{ \theta}{2} \bigg)}$

Hope It Helps

Answer 2

Answer:

The answer will be 2v sinФ / 2

Pls MARK AS BRAINLIEST

Explanation:

For change in Velocity in vectors we use formula:-

| R² | = V2+V1-2AB cosФ                      

        = V2² + V1² - 2 V x V cosФ

       = V² + V² - 2V² cosФ

        = 2 V² - 2V² cosФ

         = 2V²  [1- cosФ]                             [1-cosФ = 2 sin²Ф/2]

         = 2V² x 2 sin²Ф/2

         = 4V² sin²Ф/2

          =√4V² sin²Ф/2

       R = 2v sinФ/2