First slide

Power

Question

A particle is projected with a velocity , making an angle $θ$ with the horizontal. The instantaneous power of the gravitational force

Moderate

A

Varies linearly with time
B

Is constant throughout
C

Is negative for complete path
D

None of these

Solution

At any time,
$\begin{array}{l} \vec{v} = [ucos θ] \hat{i} + (us i n θ - gt) \hat{j} \\ \begin{aligned} P = \vec{F} \cdot \vec{v} & = (- mg \hat{j}) \cdot [ucos θ \hat{i} + (usin θ - gt) \hat{j}] \\ = {mg}^{2} t - mgusin θ \end{aligned} \end{array}$
Hence, power varies linearly with time.

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