Power Question?

Question

Bob can throw a 500 g rock with a speed of 30m/s. He moves his hand forward 1.0 m while doing so. What is Bob's maximum power output as he throws the rock?

Answer 1

Mass of the rock = 0.5 kg
Initial Velocity = 0 m/s
Final velocity = 30 m/s
Dist. travelled = 1 m
Acceleration,
v² - u² = 2as
30² - 0² = 2 x a x 1
900 = 2a
a = 900 / 2 = 450 m/s²
Time taken to reach this acceleration:
v = u + at
30 = 0 + 450 x t
t = 30 / 450 = 0.067 sec
Work done = Force x Dist.
....................= .5 x 450 x 1
....................= 225 joules
Power = Rate of doing work
............= Work / time = 225 / 0.067
.............= 3358 watt = 3.358 kw
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Answer 2

Power the product of energy per unit distance and velocity of the moving force.
Energy =Mass x Velocity square
Force is energy per meter = 225 newtons
Velocity of the force =30meters/seconds

Power =225 x 30=6750 kg meter ^2/sec^3

The time that the mass traveled is distance traveled/velocity of the moving mass.
T=D/V =1 meter/ 30meters/sec=.03333second or 33.33microseconds.

Therefore Bob used a max Power of 6750 watts(9.051899105 horsepowers)during the period of 33.33 microseconds to give the one half kilo rock mass a motional energy of 225 joules.
Energy of motion = power x time=6750 x 0.03333=225Joules

So Power was the cause of motion of the Rock.
As anything else in the Universe it take Power to move or deviate the motion of Celestial mass structures.

Very vely good question.
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