The third side ( v earth) can be determined from basic knowledge. Two sides of this triangle are given ( v asteroid and v impact). This idea is central to the field of analytical geometry. Motion in two dimensions can be thoroughly described with two independent one-dimensional equations. This example is a perfect illustration of an idea to be presented in the next section of this book. This swimmer will always cross the river in 50 s regardless of the speed of the river. The only factors that matter are the speed of the swimmer and the width of the river. The time it takes to cross a river by a swimmer swimming straight across is independent of the speed of the river. There's an interesting sideline to this question that astute readers might have noticed when looking at the first ratio in the chain of three shown above. It also works along the resultant direction… t = It works along either of the component directions… t = The only question is which distance and which speed should we use? The simple answer is pick the pair you like the best, just be sure they point in the same direction. This is why we should probably use the words displacement and velocity instead of distance and speed. This is a vector problem, so direction matters. By now you should understood that time is the ratio of displacement to velocity. Be sure to indicate that the resultant lies on a particular side of this vector for clarity. I suggest using the angle between the resultant velocity and the displacement vector that points directly across the river, but this is just my preference. The only thing open to discussion is our choice of angle. v 2 =ĭirection angles are often best determined using the tangent function. xĭetermining the resultant velocity is a simple application of Pythagorean theorem. Since speed and distance are directly proportional, the ratio of the downstream distance to the width of the river is the same as the ratio of the current speed to the swimmer's speed. Why does the acceleration due to gravity g=9.Since distance and velocity are directly proportional, this begins as a similar triangles problem. * Note that the force of gravity between two objects is dependent on the masses of the objects and the distance between them. The force is always directly proportional to the product of their masses and i nversely proportional to the square of the distance between them. The most important number in this equation is G, the universal gravitational constant, which is always equal to 6.67 * 10-11 (N * m2)/(kg2) Since this equation tends to deal with huge objects, M1 & M2 are both measured in kilograms (kg), but is measured in meters (m) as in all other equations in this unit. The magnitude of the force is the same on each, consistent with Newton's third law.įor two bodies having masses M1 and M2 with a distance r between their centers of mass, the equation for Newton's universal law of gravitation is shown in Figure 3. * Gravitational attraction is along a line joining the centers of mass of these two bodies. Newton’s universal law of gravitation states that every particle in the universe attracts every other particle with a force along a line joining them. This means for projectile motion, the starting velocity in the x-direction will be the same as the final velocity in the x-direction, while the starting and ending velocities in the y-direction will be different because of acceleration due to gravity. * Horizontal motion has constant velocity and zero acceleration while vertical motion has constant acceleration. These motions can only be related by the time variable t. An object's horizontal position, velocity, or acceleration does not affect its vertical position, velocity, or acceleration. * In Projectile Motion, what happens in the vertical direction (y-direction) does NOT affect the horizontal direction (x-direction), and vice versa. Projectile Motion - Movement of an object through the air, subject only to effects of gravity. Trajectory - The path of a projectile, which is parabolic in two dimensions Projectile - Object moving through the air, either initially thrown or dropped, subject only to the effects of gravity
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