This line is represented as a straight horizontal line in the diagrams. There is no acceleration in this direction of the motion since gravity only acts vertically on the object. The range of the projectile is defined as the displacement in the horizontal direction of the motion of the object. So 45 degrees is the only or the best angle at which the maximum height of the projectile can be achieved for any object or projectile following a trajectory under projectile motion. We can solve this quite easily by differentiating the formula and equating it with zero hence getting the answer as 45 degrees. With the help of formulas, one can calculate at which angle an object or projectile be thrown so that it gains maximum height. The net of both cos and sin is taken as the final angle in the calculations. And cos(α)stands for the horizontal component of the angle.sin(α): stands for the vertical component of the angle.h is the net height from which the object or the projectile has been thrown.V₀ is the vertical velocity of the object under influence of external force.The formula for the projectile range hence may be written as d = V₀ * cos(α) * / g In this particular case, the time spent flying upwards is much shorter than the time when the object is falling down in the same trajectory (time from reaching the maximum height to striking the ground in the same projectile or trajectory). Launch from an elevation (in this case the initial height > 0) And hence this formula can be used as the standard formula for determining the range of the object under the influence of external force from a net height of zero.Ĭase 2. Knowing the trigonometric identity of sin(2 * x) = 2 * sin(x) * cos(x), we can rewrite the final formula as d = V₀² * sin(2 * α) / g. Velocity in our case is the horizontal velocity Vx = V0 * cos(α), and time to reach the ground is a value we've already calculated is as followĭ = V * t = V₀ * cos(α) * 2 * V₀ * sin(α) / g
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |