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Byju's Answer

Standard XII

Physics

The Equation for the Path of Projectile

For a particl...

Question

For a particle moving in the x – y plane, the X and Y coordinate are changing as $X = a s i n ω t$ and $y = a (1 - c o s ω t)$ , where `a` and $ω$ are constants. Then, what can be inferred for the trajectory of the particle?

The trajectory is parabolic

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The trajectory is elliptical

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The trajectory is such that distance moved by the particle is directly proportional to time

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The trajectory of the particle is equidistant from the origin at every instant of time.

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Solution

The correct option is C
The trajectory is such that distance moved by the particle is directly proportional to time

$x^{2} + (y - a)^{2} = a^{2}$
So, it moves in circle with uniform speed.

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For a particle moving in the x – y plane, the X and Y coordinate are changing as X=a sinωt and y=a(1−cosωt), where `a` and ω are constants. Then, what can be inferred for the trajectory of the particle?

The correct option is C The trajectory is such that distance moved by the particle is directly proportional to time x2+(y−a)2=a2 So, it moves in circle with uniform speed.

For a particle moving in the x – y plane, the X and Y coordinate are changing as $X = a s i n ω t$ and $y = a (1 - c o s ω t)$ , where `a` and $ω$ are constants. Then, what can be inferred for the trajectory of the particle?

The correct option is C
The trajectory is such that distance moved by the particle is directly proportional to time

$x^{2} + (y - a)^{2} = a^{2}$
So, it moves in circle with uniform speed.