Question

A plane is moving with velocity be taken by θ angle and its speed domains find change in velocity of plane .​

Answer 1

Correct question

A plane is moving with velocity v taken by θ angle and its speed remains v. find change in velocity of plane .

Answer:  

$\bf{\boxed{\boxed{\huge\it{2vsin\frac{\theta}{2}}}}}$

Explanation:

given that,

A plane is moving with velocity v taken by θ angle and its speed remains v

we know that,

change in velocity = V2 - V1

according to the figure,

for -V1 sliding V1 opposite side,

now,

V2  - V1 =

$\large{\sqrt{{v}^{2}+{v}^{2}-2{v}^{2}cos\theta}}$

$\sqrt{2{v}^{2}-2{v}^{2}\cos \theta}$

$\sqrt{2{v}^{2}(1-cos\theta)}$

$v\sqrt{2(1-cos\theta)}$

we know that,

$1-cos\theta\:=\:2{sin}^{2}  \frac{\theta}{2}$

putting the values,

$v\sqrt{2\times2{sin}^{2}\frac{\theta}{2}}$

$v\sqrt{4{sin}^{2}\frac{\theta}{2}}$

$\boxed{\large\bf\it{2vsin \frac{\theta}{2}}}$

so,

V2 - V1 = $\huge\bf\it{2vsin\frac{\theta}{2}}$

so,

change in velocity,

= $\bf{\boxed{\boxed{\huge\it{2vsin \frac{\theta}{2}}}}}$