Parabolic Trajectory
Parabolic Trajectory - Related Videos
16:14
Trajectory Data Analyses for Pedestrian Space-time Activity Study
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Cited by 15 •
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A suite of spatiotemporal processing methods are presented to analyze human trajectory data, such as that collected using a GPS device, for the purpose of modeling pedestrian space-time activities.
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Orthogonal Trajectories
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2026
Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
04:24
Studying Cell Rolling Trajectories on Asymmetric Receptor Patterns
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We describe a protocol to observe and analyze cell rolling trajectories on asymmetric receptor-patterned substrates. The resulting data are useful for engineering of receptor-patterned substrates for label-free cell separation and analysis.
10:04
Electroporation of the Hindbrain to Trace Axonal Trajectories and Synaptic Targets in the Chick Embryo
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Cited by 9 •
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How neuronal networks are established in the embryonic brain is a fundamental question in developmental neurobiology. Here we combined an electroporation technique with novel genetic tools, such as Cre/Lox–plasmids and PiggyBac-mediated DNA transposition system in the avian hindbrain to label dorsal interneurons and track their axonal projections and synaptic targets at various developmental stages.
07:52
Automated Rat Single-Pellet Reaching with 3-Dimensional Reconstruction of Paw and Digit Trajectories
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Cited by 27 •
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Rodent skilled reaching is commonly used to study dexterous skills, but requires significant time and effort to implement the task and analyze the behavior. We describe an automated version of skilled reaching with motion tracking and three-dimensional reconstruction of reach trajectories.
FAQs
Treating the launch velocity as horizontal and vertical components makes the motion easier to analyze. The horizontal component sets how quickly the object advances, while the vertical component controls its upward and downward motion under gravity. Combining the two component motions at the same time gives the object's position, allowing range, height, and impact location to be predicted from launch conditions.
The horizontal position advances steadily, while vertical position changes under constant downward acceleration. At the same elapsed time, each horizontal position corresponds to a vertical position determined by gravity. Combining these paired positions produces the parabolic shape, provided gravity remains dominant and the gravitational field is approximately uniform.
The initial velocity and its division between horizontal and vertical components strongly influence the outcome. Changing the horizontal component primarily alters how far the object travels, whereas changing the vertical component primarily affects its rise and flight duration. Gravity sets the downward acceleration, so recording launch speed, direction, and relevant gravitational conditions supports accurate predictions.
Begin by recording the launch conditions, especially the initial velocity and its horizontal and vertical components. Analyze horizontal motion separately from the downward acceleration caused by gravity, then combine both positions at equal times. The resulting prediction can provide range, maximum height, flight time, and impact position for comparison with observations.
An experiment should record the initial velocity, its direction, and the object's positions during flight. Measurements of range, maximum height, flight time, and impact position can then be compared with the model's predictions. Agreement tests whether gravity-dominated motion and the assumed approximately uniform gravitational field describe the observed projectile well.
Parabolic Trajectory analysis supports studies of thrown objects, launched projectiles, sports performance, and engineering designs. In physics experiments, it provides a practical way to examine Newtonian mechanics by comparing measured motion with predictions based on launch conditions and gravity. Its value is greatest when gravity remains the dominant force and the gravitational field is approximately uniform.