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The Euler’s pump and turbine equations are most fundamental equations in the field of turbo-machinery. These equations govern the power, efficiencies and ... more

where **Vt** is the terminal velocity,
**m** is the mass of the skydiver,
**g** is the acceleration due to gravity,
**C _{d}** is the drag coefficient,

**ρ**is the density of the fluid through which the object is falling, and

**A**is the projected area of the object.

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.

http://openstaxcollege.org/textbooks/college-physics

Creative Commons License : http://creativecommons.org/licenses/by/3.0/

where h is skydiver height and w the width at “spread-eagle” position

Gyration is a rotation in a discrete subgroup of symmetries of the Euclidean plane such that the subgroup does not also contain a reflection symmetry whose ... more

A horn antenna or microwave horn is an antenna that consists of a flaring metal waveguide shaped like a horn to direct radio waves in a beam. Horns are ... more

A right prism is a prism in which the joining edges and faces are perpendicular to the base faces. The volume of a right prism whose base is a regular ... more

Centripetal force (from Latin centrum “center” and petere “to seek”) is a force that makes a body follow a curved path: its ... more

Aperture is a “hole” or an opening through which light travels. The aperture of an optical system is the opening that determines the cone angle ... more

Prism is a polyhedron with an n-sided polygonal base, a translated copy (not in the same plane as the first), and “n” other faces (necessarily ... more

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:

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

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:

For **y** axis:

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/

Centripetal force (from Latin centrum “center” and petere “to seek”) is a force that makes a body follow a curved path: its ... more

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Find the terminal velocity of an

85-kgskydiver falling in a spread-eagle position.