Ballistic Seed Dispersal. Some plants disperse their seeds...

Ballistic Seed Dispersal. Some plants disperse their seeds when the fruit splits and contracts, propelling the seeds through the air. The trajectory of these seeds can be determined with a high-speed camera. In an experiment on one type of plant, seeds are projected at $20 \mathrm{~cm}$ above ground level with initial speeds between $2.3 \mathrm{~m} / \mathrm{s}$ and $4.6 \mathrm{~m} / \mathrm{s}$ The launch angle is measured from the horizontal, with $+90^{\circ}$ corresponding to an initial velocity straight up and $-90^{\circ}$ straight down. If a seed is launched at an angle of $0^{\circ}$ with the maximum initial speed, how far from the plant will it land? Ignore air resistance, and assume that the ground is flat. (a) $20 \mathrm{~cm} ;$ (b) $93 \mathrm{~cm} ;$ (c) $2.2 \mathrm{~m}$; (d) $4.6 \mathrm{~m}$.

Ballistic Seed Dispersal. Some plants disperse their seeds when the fruit splits and contracts, propelling the seeds through the air. The trajectory of these seeds can be determined with a high-speed camera. In an experiment on one type of plant, seeds are projected at $20 \mathrm{~cm}$ above ground level with initial speeds between $2.3 \mathrm{~m} / \mathrm{s}$ and $4.6 \mathrm{~m} / \mathrm{s}$ The launch angle is measured from the horizontal, with $+90^{\circ}$ corresponding to an initial velocity straight up and $-90^{\circ}$ straight down.
If a seed is launched at an angle of $0^{\circ}$ with the maximum initial speed, how far from the plant will it land? Ignore air resistance, and assume that the ground is flat. (a) $20 \mathrm{~cm} ;$ (b) $93 \mathrm{~cm} ;$ (c) $2.2 \mathrm{~m}$;
(d) $4.6 \mathrm{~m}$.

Key Concepts

Launch from an Elevation

Launching a projectile from an elevated position (i.e., not starting at ground level) introduces an initial vertical displacement that affects the time of flight and the range. The initial height must be taken into account when solving the equations of motion to determine where the projectile will land.

Horizontal Range Calculation

The horizontal range of a projectile is the distance it travels along the horizontal axis from its launch point to where it lands. It is determined by the product of the horizontal velocity and the total time the projectile is in the air, which may be computed by solving for the time of descent using the kinematic equations for the vertical motion.

Projectile Motion

Projectile motion describes the motion of an object that is launched into the air and is influenced only by gravity (ignoring air resistance). This concept involves analyzing the object’s path, known as its trajectory, by breaking its motion into horizontal and vertical components, which are influenced independently by the initial conditions and gravitational acceleration.

Kinematic Equations

Kinematic equations are used to model the motion of objects under constant acceleration. In projectile motion, these equations help calculate quantities such as the time of flight, maximum height, and horizontal range by relating displacement, initial velocity, acceleration due to gravity, and time.

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