In a video game, two objects move around the screen according to the equations r = 4cos(0) and r= -1 + 2cos(0). Which coordinates represent a possible collision point of the objects?

Hence, The coordinate that represents a possible collision point of the objects in the form (-2, )

Given that ,

The first object is moving around the screen r = 4 cos(0)

The second object is moving around the screen r = -1 + 2cos(0)

We have to find ,

The coordinates represent a possible collision point of the objects.

According to the question,

Coordinate represent collision points to object ,

Equating both equations ;

4·cos(θ) = -1 + 2·cos(θ)

4·cos(θ) - 2·cos(θ) = -1

2·cos(θ) = -1

cos(θ) = -

θ = = 120°

=

Therefore, the two equations are equal when θ =

We have;

r = 4·cos() = -2

And r = -1 + 2·cos() =

r = -2

r = 4·cos() = -1 + 2·cos()

r = -2

The coordinate that represents a possible collision point of the objects in the form (r, θ) is therefore r = -2 and .

Hence, The coordinate that represents a possible collision point of the objects in the form (-2, ) .

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The correct option is;

Step-by-step explanation:

The given parameters are

The equation of motion of one (the first) object is r = 4·cos(θ)

The equation of motion of the other (the second) object is r = -1 + 2·cos(θ)

Equating both equations gives;

4·cos(θ) = -1 + 2·cos(θ)

4·cos(θ) - 2·cos(θ) = -1

2·cos(θ) = -1

cos(θ) = -1/2

θ = Arccos(-1/2) = 120° = 2·π/3

Therefore, the two equations are equal when θ = 2·π/3 for which we have;

r = 4·cos(2π/3) = -2 and r = -1 + 2·cos(2π/3) = -2

∴ r = 4·cos(2π/3) = -1 + 2·cos(2π/3) = -2

The coordinate that represents a possible collision point of the objects in the form (r, θ) is therefore