(C) The velocity components are obtained by differentiating the position equations with respect to time $t$.$v_x = \frac{dx}{dt} = \frac{d}{dt}(6t) =

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(C) The velocity components are obtained by differentiating the position equations with respect to time $t$.$v_x = \frac{dx}{dt} = \frac{d}{dt}(6t) = 6 \ m/s$.$v_y = \frac{dy}{dt} = \frac{d}{dt}(8t - 5t^2) = 8 - 10t \ m/s$.At the time of projection,$t = 0$.Substituting $t = 0$ into the velocity components:$v_x = 6 \ m/s$.$v_y = 8 - 10(0) = 8 \ m/s$.The magnitude of the initial velocity $v$ is given by $v = \sqrt{v_x^2 + v_y^2}$.$v = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \ m/s$.

Class 11 Physics 3-2.Motion in Plane Horizontal Projectile Motion

Medium

The height $y$ and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = (8t - 5t^2) \ m$ and $x = 6t \ m$,where $t$ is in seconds. The velocity with which the projectile is projected is ......... $m/s$.

A
$8$
B
$6$
C
$10$
D
Not obtainable from the data

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3-2.Motion in Plane

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Horizontal Projectile Motion

$A$ projectile is thrown at an angle $\theta$ such that it is just able to cross a vertical wall of height $H$ at its highest point,as shown in the figure. The horizontal distance from the point of projection to the wall is $\sqrt{3} H$. The angle $\theta$ at which the projectile is thrown is given by:

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Three balls of same masses are projected with equal speeds at angles $15^{\circ}, 45^{\circ}$,and $75^{\circ}$. If their ranges are $R_1, R_2$,and $R_3$ respectively,then:

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For a given angle of the projectile,if the initial velocity is doubled,the range of the projectile becomes:

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Define a projectile and derive the equation of its trajectory: $y = (\tan \theta_0)x - \frac{g}{2(v_0 \cos \theta_0)^2}x^2$.

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$A$ body is projected at an angle of $30^{\circ}$ with the horizontal with momentum $p$. At its highest point,the magnitude of the momentum is

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The height $y$ and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = (8t - 5t^2) \ m$ and $x = 6t \ m$,where $t$ is in seconds. The velocity with which the projectile is projected is ......... $m/s$.

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Three balls of same masses are projected with equal speeds at angles $15^{\circ}, 45^{\circ}$,and $75^{\circ}$. If their ranges are $R_1, R_2$,and $R_3$ respectively,then:

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