Assertion (A): The velocity of a projectile a | vedclass

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(D) The trajectory of a projectile is given by the equation:$y = f(x) = x 	an 	heta - \frac{g x^2}{2 u^2 \cos^2 	heta}$The slope of the trajectory

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$A$ is false but $R$ is true

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(D) The trajectory of a projectile is given by the equation:$y = f(x) = x 	an 	heta - \frac{g x^2}{2 u^2 \cos^2 	heta}$The slope of the trajectory at any point $(x, y)$ is given by the derivative $\frac{dy}{dx}$:$\frac{dy}{dx} = 	an 	heta - \frac{gx}{u^2 \cos^2 	heta} = \frac{v_y}{v_x}$This slope represents the ratio of the vertical component of velocity to the horizontal component of velocity,not the magnitude of the velocity itself. Therefore,Assertion $(A)$ is incorrect.Reason $(R)$ states that the velocity vector at any point is always along the tangent to the trajectory at that point. This is a fundamental property of motion in a plane,as the instantaneous velocity is defined as the rate of change of position,which is directed along the tangent to the path. Thus,Reason $(R)$ is correct.

Assertion $(A)$: The velocity of a projectile at a point on its trajectory is equal to the slope at that point.
Reason $(R)$: The velocity vector at a point is always along the tangent to the trajectory at that point.

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Assertion $(A)$: The velocity of a projectile at a point on its trajectory is equal to the slope at that point.Reason $(R)$: The velocity vector at a point is always along the tangent to the trajectory at that point.