Question

PLS HELP ME IN THIS its so tuff

Answer 1

Answer :

• Initial Velocity = vᵢ
• Angle of projection = θ

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Average Velocity :

$\sf :\implies v_{avg} = \dfrac{v_f+v_i}{2}$

$\sf :\implies v_{avg} = \dfrac{v \ cos\theta\hat{i} + v \ cos\theta\hat{i} + v \ sin\theta\hat{j}}{2}$

$\sf :\implies v_{avg} = \dfrac{2v \ cos\theta\hat{i} + v \ sin\theta\hat{j}}{2}$

Its Magnitude :

$\sf :\implies v_{avg} = \sqrt{\bigg\lgroup\dfrac{(2v \ cos\theta)^2}{2^2}\bigg\rgroup + \bigg\lgroup\dfrac{(2v \ sin\theta)^2}{2^2}\bigg\rgroup}$

$\sf :\implies v_{avg} = \dfrac{v}{2}\sqrt{4 \ cos^2\theta + sin^2\theta}$

$\sf :\implies\pink{ v_{avg} = \dfrac{v}{2}\sqrt{1+3cos^2\theta}}$

$\displaystyle\therefore\:\underline{\textsf{Answer the question is \textbf{Option C}}}$