Maximum height of projectile1/23/2024 ![]() ![]() Note that the data in the atlas were obtained between 19 from Caucasian children, which may limit how accurately the Greulich-Pyle method can be used for current children. Based on bone age, the height of the child, and the data compiled in the atlas, it is possible to predict height based on the percentage of height growth remaining at a given bone age. This method compares the radiograph of the patient to that of the nearest standard radiograph in the Greulich-Pyle atlas, a compilation of bone age data. One such method is the Greulich-Pyle method that involves left hand and wrist radiographs to measure bone age. Regardless of how accurate the method, height prediction is not an exact science, and it is possible that a child's height can deviate significantly from what is predicted.īone age can be used to predict height and is considered more accurate than the other methods listed below. Many different methods have been developed to predict a child's adult height, some more accurate than others. This is due to factors such as the decreased height of intervertebral discs as well as changes due to degenerative diseases. In some cases, a person's height begins to shrink in middle age, though shrinkage of stature is largely universal in the very elderly. On average, female and male growth trails off to zero at about 15 and 18 years old, respectively. This is typically referred to as the pubertal growth spurt. During puberty, the growth rate increases again to a second maximum, after which it slowly declines to zero. The growth rate declines rapidly from birth to roughly age 2 and declines more slowly thereafter. Other important factors that contribute to a child's adult height include nutrition, health, sports activities, health and age of the mother during pregnancy, etc. ![]() This means that very tall or short parents are likely to have a taller or shorter child than average, but the child is likely to be closer to the average height than their parents. Normally, a child's height is based on parental heights subject to regression toward the mean. Some studies suggest that genetics contributes 60%-80%. The precise contribution from these two factors is complex. The height of a person is determined by a combination of genetics and environmental factors. Therefore the horizontal distance travelled is 55."How tall will I be?" or "how tall will my child be?" are questions that are often asked. Therefore the time of flight is 2.55s (3sf)ī) The range can be found working out the horizontal distance travelled by the particle after time T found in part (a) Ī) How long will it be before the impact?ī) How far will the cannon ball travel before hitting the ground?Ī) When the particle hits the ground, y = 0.Īpplying this equation vertically, when the particle hits the ground:Ġ = 25Tsin30 - ½ gT 2 (Where T is the time of flight) To find the speed or direction of the particle at any time during the motion, find the horizontal and vertical components of the velocity using the above formulae and use Pythagoras's theorem:Ī cannon ball is fired at an angle of 30° to the horizontal at a speed of 25ms -1. The velocity of the particle at any time can be calculated from the equation v = u + at.īy applying this equation horizontally, we find that: ![]() This is because the maximum sin2a can be is 1 and sin2a = 1 when a = 45°. If a particle is projected at fixed speed, it will travel the furthest horizontal distance if it is projected at an angle of 45° to the horizontal. The time the ball is in the air is given by (3). When the particle returns to the ground, y = 0. ![]() Remember, there is no acceleration horizontally so a = 0 here. Using this equation vertically, we have that a = -g (the acceleration due to gravity) and the initial velocity in the vertical direction is usina (by resolving). The range (R) of the projectile is the horizontal distance it travels during the motion. A particle is projected at a speed of u (m/s) at an angle of a to the horizontal: The suvat equations can be adapted to solve problems involving projectiles. How far the particle travels will depend on the speed of projection and the angle of projection. When a particle is projected from the ground it will follow a curved path, before hitting the ground. ![]()
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