(D) The range of a projectile is given by $R = \frac{u^2 \sin(2\theta)}{g}$.Since the ranges are equal,$\sin(2\theta_1) = \sin(2\theta_2)$.This implie

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$\tan \theta_1 / \tan \theta_2$

(D) The range of a projectile is given by $R = \frac{u^2 \sin(2\theta)}{g}$.Since the ranges are equal,$\sin(2\theta_1) = \sin(2\theta_2)$.This implies $2\theta_1 = 180^\circ - 2\theta_2$,which simplifies to $\theta_1 + \theta_2 = 90^\circ$,or $\theta_2 = 90^\circ - \theta_1$.The time of flight is given by $T = \frac{2u \sin \theta}{g}$.The ratio of the times of flight is $\frac{T_1}{T_2} = \frac{\frac{2u \sin \theta_1}{g}}{\frac{2u \sin \theta_2}{g}} = \frac{\sin \theta_1}{\sin \theta_2}$.Since $\theta_2 = 90^\circ - \theta_1$,we have $\sin \theta_2 = \sin(90^\circ - \theta_1) = \cos \theta_1$.Thus,$\frac{T_1}{T_2} = \frac{\sin \theta_1}{\cos \theta_1} = \tan \theta_1$.

Class 11 Physics 3-2.Motion in Plane Mix Examples-Motion in Plane

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If two bodies $A$ and $B$ are projected with the same velocity $u$ but with different angles $\theta_1$ and $\theta_2$ respectively with the horizontal such that both have the same range,then the ratio of the times of flight of the bodies $A$ and $B$ is:

AP EAMCET 2025 All AP EAMCET

A
$\sin \theta_2 / \sin \theta_1$
B
$\sin \theta_1 / \sin \theta_2$
C
$\tan \theta_2 / \tan \theta_1$
D
$\tan \theta_1 / \tan \theta_2$

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If two bodies $A$ and $B$ are projected with the same velocity $u$ but with different angles $\theta_1$ and $\theta_2$ respectively with the horizontal such that both have the same range,then the ratio of the times of flight of the bodies $A$ and $B$ is:

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$A$ particle moves in a plane along an elliptic path given by $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. At point $(0, b)$,the $x$-component of velocity is $u$. The $y$-component of acceleration at this point is

$A$ body is moving with an initial velocity of $10 \sqrt{2} \ m/s$ in the north-east direction. If it is subjected to an acceleration of $2 \ m/s^2$ directed towards the south, then the velocity of the body after $5 \ s$ is:

Two bodies were thrown simultaneously from the origin: one straight up and the other at an angle of $60^{\circ}$ to the vertical. The initial velocity of each body is $10 \ m \ s^{-1}$. Neglecting air resistance, the distance between the two bodies after $t=2 \ s$ is (Use $g=10 \ m \ s^{-2}$):

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