Greenwood press
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book-20600
ANGLE
3 30° North of West 60° West of North Alternate methods of denoting direction when a boat is 3 miles from shore and 6 miles from its destination. The navigation angle, β, of a boat based on its distance from shore, s, and the distance from its final destination, d, is equal to arccos( s d ). Angles are useful for reflecting light rays or objects off of flat objects. The angle by which an object, such as a ball, approaches a wall is equal to the angle by which the object bounces off the wall. This is true because a ball’s reflection off a wall will be the same distance away from the wall as if it had gone in a straight line. In essence, reflections preserve congruence. By the transitive prop- erty, the angle of the ball coming into the wall will equal the angle of the ball leaving the wall, as shown below. In billiards or miniature golf, a player can use this principle when aiming for a hole by simply aiming for the hole’s reflection. Athletes who try to throw or hit balls certain distances, such as baseballs, bas- ketballs, footballs, and golf balls, use angles strategically. If they want to hit a ball short and high, they will use an angle close to 90°. In order to hit a low-fly- ing line drive, they will use an angle close to 0°. The horizontal distance in meters, x, of an object can be determined by the product of its initial velocity in meters per second, v 0 , the time in seconds, t, that the ball is in the air, and the cosine of the angle, α, it is released or hit. Since the earth’s gravitational force pulls a ball towards the surface, the vertical distance in meters, y, also needs to be considered in order to determine the ideal angle at which to release or hit a ball. The two equations describing the path of the ball in both directions are rep- resented as x = v 0 t cos α y = v 0 t sin α − 4.9t 2 . The ball will be on the ground when y is 0. Solving the second equation for the time t that will provide this value gives t = 0 or t = 1 4.9 v 0 sin α. The latter solu- tion gives the time the ball will be in the air. Substituting in the equation for x Download 1.81 Mb. Do'stlaringiz bilan baham: |
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