A particle of mass m is projected at an angle | vedclass

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Question

(C) The force of gravity acting on the particle is $\vec{F} = -mg \hat{j}$.At the highest point,the vertical displacement of the particle is equal to

Vedclass · Accepted Answer

$-\frac{m u^2 \sin^2 \alpha}{2}$

Vedclass · Answer

(C) The force of gravity acting on the particle is $\vec{F} = -mg \hat{j}$.At the highest point,the vertical displacement of the particle is equal to the maximum height $H$.The formula for maximum height is $H = \frac{u^2 \sin^2 \alpha}{2g}$.The work done by gravity is given by the product of the force and the vertical displacement: $W = \vec{F} \cdot \vec{S} = (-mg) 	imes H$.Substituting the value of $H$: $W = -mg \left( \frac{u^2 \sin^2 \alpha}{2g} ight)$.Simplifying the expression,we get $W = -\frac{m u^2 \sin^2 \alpha}{2}$.

$A$ particle of mass $m$ is projected at an angle $\alpha$ to the horizontal with initial velocity $u \ m/s$. What is the work done by gravity during the time it reaches its highest point?

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