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Q.

A particle (mass m) is projected with an initial velocity v at an angle $θ$ to the horizontal. What is the work done by the force of gravity from the instant of throwing to the instant it reaches the highest point?

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a

zero

b

$m v^{2} \sin θ$

c

-m $v^{2} \sin$ $θ$

d

$- \frac{m v^{2} \sin^{2} θ}{2}$

answer is D.

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Detailed Solution

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$W_{m g} =$ $K_{f}$ - $K_{i}$ = $\frac{1}{2}$ m(v cos $θ$ $)^{2}$ - $\frac{1}{2}$ $m v^{2}$

= $\frac{1}{2} m v^{2}$ [ $\cos^{2} θ - 1$ ] = - $\frac{1}{2} m v^{2} \sin^{2} θ$

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