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Alla [95]
3 years ago
6

Find the polar angle (in radians with respect to +x-axis) of −3i + j.

Physics
1 answer:
Gala2k [10]3 years ago
5 0

Answer:

-18.43^{\circ}

Explanation:

Let \theta be the polar angle of −3i + j. We can find it using the formula as follows :

\tan\theta=\dfrac{y}{x}\\\\\tan\theta=\dfrac{1}{-3}\\\\\theta=\tan^{-1}(\dfrac{1}{-3})\\\\\theta=-18.43^{\circ}

So, the required polar angle is -18.43^{\circ}.

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A 0.500-kg potato is fired at an angle of 80.0° above the horizontal from a PVC pipe used as a "potato gun" and reaches a height
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Answer:

(a) 47.15ms^{-1}

(b) 2470.13ms^{-2}

(c) 1235.06N and 252.05 as a ratio

Explanation:

From Newton's second law of motion

F=ma where m is mass, a is acceleration and F is net force

Also from kinetic equation of motion, velocity and displacement are related using equation

v^{2}=u^{2}+2sa

Where v is final velocity, u is initial velocity, a is acceleration and s is displacement

From the free body diagram attached, final velocity at maximum height is 0 and initial velocity is usin80^{o}

Also, the vertical component can be written as

v_{y}^{2} }=u_{y}^{2} } -2gs The negative sign before 2gs means displacement is opposite the gravitational force

Where g is acceleration due to gravity,u_{y} is vertical component of initial velocity and v_{y} is vertical component of final velocity

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u_{y}^{2} } =2gs

s=110 and g is taken as 9.8

u_{y}=\sqrt{2*9.8*110}=46.43275

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Also, it's evident that the vertical component of initial velocity is u_{y}=u_{i}sin \theta where \theta is angle of projection and u_{i} is resultant velocity

Making u_{i} the subject we obtain u_{i}=\frac {u_{y}}{sin \theta}

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(b)

Displacement depends on length of tube hence s=0.450m hence going back to kinetic equation v^{2}=u^{2}+2sa

The final velocity v is answer in part a which is 47.15ms^{-1}, initial velocity u is 0ms^{-1} hence the equation is re-written as

v^{2}=2sa and making a the subject we obtain

a=\frac {v^{2}}{2s}

a=\frac {47.15^{2}}{2*0.450}=2470.13ms^{-2}

Therefore, average acceleration is 2470.13ms^{-2}

(c)

From Newton's second law of motion, F=ma where m=0.500kg and a is 2470.13ms^{-2}

Therefore, the average force of potato is

F=0.5*2470.13=1235.06N

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Taking R as ratio of average force and weight of potato

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R=\frac {1235.06}{0.500*9.8}=252.05

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An early method of measuring the speed of light makes use of a rotating slotted wheel. A beam of light passes through one of the
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