A particle is projected with a velocity of 30 | vedclass

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(D) Given: Initial velocity $u = 30\,m/s$,angle $	heta_0 = 	an^{-1}(3/4)$.From $	an	heta_0 = 3/4$,we have $\sin	heta_0 = 3/5$ and $\cos	heta_0 =

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$1/3$

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(D) Given: Initial velocity $u = 30\,m/s$,angle $	heta_0 = 	an^{-1}(3/4)$.From $	an	heta_0 = 3/4$,we have $\sin	heta_0 = 3/5$ and $\cos	heta_0 = 4/5$.Initial horizontal component: $u_x = u \cos	heta_0 = 30 	imes (4/5) = 24\,m/s$.Initial vertical component: $u_y = u \sin	heta_0 = 30 	imes (3/5) = 18\,m/s$.After $t = 1\,s$,the horizontal velocity remains constant: $v_x = u_x = 24\,m/s$.The vertical velocity changes due to gravity: $v_y = u_y - gt = 18 - (10 	imes 1) = 8\,m/s$.The angle $	heta$ with the horizontal is given by $	an	heta = v_y / v_x$.Substituting the values: $	an	heta = 8 / 24 = 1/3$.

$A$ particle is projected with a velocity of $30\,m/s$ at an angle of $\theta_0 = \tan^{-1}(3/4)$. After $1\,s$,the particle is moving at an angle $\theta$ to the horizontal. What is the value of $\tan\theta$? (Take $g = 10\,m/s^2$)

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