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Freefall in Uniform Gravitational Field with Air Resistance (velocity)

Free fall is any motion of a body where its weight is the only force acting upon it. In Uniform gravitational field with air resistance the air resistance ... more

Trajectory Range

A trajectory or flight path is the path that a moving object follows through space as a function of time. A trajectory can be described mathematically ... more

Velocity at a distance x (for object following a ballistic trajectory)

A trajectory or flight path is the path that a moving object follows through space as a function of time. A trajectory can be described mathematically ... more

Time of flight for a projectile following a ballistic trajectory

A trajectory or flight path is the path that a moving object follows through space as a function of time. ballistic trajectory of a projectile is the path ... more

Trajectory Height

A trajectory or flight path is the path that a moving object follows through space as a function of time. A trajectory can be described mathematically ... more

True Airspeed - Low-speed flight

The true airspeed (TAS; also KTAS, for knots true airspeed) of an aircraft is the speed of the aircraft relative to the airmass ... more

Hole change in Gibbs free energy

In chemistry, a reaction quotient: Qr is a function of the activities or concentrations of the chemical species involved in a chemical reaction. In the ... more

Equivalent airspeed (in function of dynamic pressure)

Equivalent airspeed (EAS) is the airspeed at sea level in the International Standard Atmosphere at which the dynamic pressure is ... more

Orbit Equation

In astrodynamics an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. ... more

Worksheet 334

In a video game design, a map shows the location of other characters relative to the player, who is situated at the origin, and the direction they are facing. A character currently shows on the map at coordinates (-3, 5). If the player rotates counterclockwise by 20 degrees, then the objects in the map will correspondingly rotate 20 degrees clockwise. Find the new coordinates of the character.

To rotate the position of the character, we can imagine it as a point on a circle, and we will change the angle of the point by 20 degrees. To do so, we first need to find the radius of this circle and the original angle.

Drawing a right triangle inside the circle, we can find the radius using the Pythagorean Theorem:

Pythagorean theorem (right triangle)

To find the angle, we need to decide first if we are going to find the acute angle of the triangle, the reference angle, or if we are going to find the angle measured in standard position. While either approach will work, in this case we will do the latter. By applying the cosine function and using our given information we get

Cosine function
Subtraction

While there are two angles that have this cosine value, the angle of 120.964 degrees is in the second quadrant as desired, so it is the angle we were looking for.

Rotating the point clockwise by 20 degrees, the angle of the point will decrease to 100.964 degrees. We can then evaluate the coordinates of the rotated point

For x axis:

Cosine function

For y axis:

Sine function

The coordinates of the character on the rotated map will be (-1.109, 5.725)

Reference : PreCalculus: An Investigation of Functions,Edition 1.4 © 2014 David Lippman and Melonie Rasmussen
http://www.opentextbookstore.com/precalc/
Creative Commons License : http://creativecommons.org/licenses/by-sa/3.0/us/

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