First slide

Power

Question

A particle is projected with a velocity u 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,
$\vec{v} = [u \cos θ] \hat{i} + (u \cos θ - g t) \hat{j}$
$P = \vec{F} . \vec{v} = (- m g \hat{j}) . [u \cos θ \hat{i} + (u \sin θ - g t) \hat{j}]$
$m g^{2} t - m g u s i n θ$
Hence, power varies linearly with time.

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