# The equations of motion of the point x = cos t and y = 2 sin t are given.

**The equations of motion of the point x = cos t and y = 2 sin t are given. Determine the distance from the point to the origin at the time t = 2.5 s.**

To determine the distance S from some material point to the origin of coordinates, it is necessary to determine its coordinates (x; y) at a given time t = 2.5 s, then use the formula: S = √ (x ^ 2 + y ^ 2).

From the condition of the problem it is known that the motion of a point is given by the equations: x = cos t and y = 2 ∙ sin t, then:

S = √ ((cos t) ^ 2 + (2 ∙ sin t) ^ 2) or S = √ ((cos t) ^ 2 + 4 ∙ (sin t) ^ 2). Substitute the values of the quantities into the calculation formula:

S = √ ((- 0.8011) ^ 2 + 4 ∙ 0.5986 ^ 2);

S ≈ 1.44 m.

Answer: the distance from a given material point to the origin of coordinates at a specified moment in time is ≈ 1.44 meters.