Question

An object moves around x + y = 25 (which represents a

circle whose radius is 5 meters) at a constant speed. At time
t = 0 seconds, the object is at (5,0). When t = 1, it is at (4,3). Where is the object when t = 2? When t = 3? when t = n?
What is the object’s speed? At what times does the object return to (5, 0)? To arrive at your answers, what assumptions did you make?

Answer 1

Explanation:

There is an error in the question.

x + y = 25 is NOT the equation of a circle.

It should be x^2 + y^2 = 5^2.

Parametric equations for the circle:

x = 5cosθ

y = 5sinθ

After 1 second, the object is at (4,3), so θ=arctan(3/4).

At 2 seconds, θ=2arctan(3/4). The object is at (5cosθ,5sinθ) = (1.4, 4.8).

At 3 seconds, θ=3arctan(3/4). The object is at (-1.76, 4.68).

360°/arctan(3/4) ≈ 9.764

The object returns to (5,0) after 9.764 seconds.