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. About how long does it take a seed launched at $90^{\circ}$ at the highest possible initial speed to reach its maximum height? Ignore air resistance. (a) $0.23 \mathrm{~s} ;$ (b) $0.47 \mathrm{~s} ;$ (c) $1.0 \mathrm{~s}$; d) $2.3 \mathrm{~s}$.

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.
About how long does it take a seed launched at $90^{\circ}$ at the highest possible initial speed to reach its maximum height? Ignore air resistance. (a) $0.23 \mathrm{~s} ;$ (b) $0.47 \mathrm{~s} ;$ (c) $1.0 \mathrm{~s}$; d) $2.3 \mathrm{~s}$.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Projectile Motion

Projectile motion describes the trajectory of an object moving through space under the influence of gravity alone. This concept is foundational in physics for analyzing how objects move when launched, taking into account factors such as launch angle, initial speed, and gravitational acceleration.

Vertical Motion

Vertical motion is a specific case of projectile motion where the object is launched straight up. In this scenario, only the vertical component of the motion is considered, which simplifies the analysis as there is no horizontal displacement.

Acceleration Due To Gravity

Acceleration due to gravity is the constant rate in which an object accelerates downward while in free fall near the Earth's surface, typically approximated as 9.8 m/s². This key concept is used to determine how long it takes for an object to decelerate as it ascends in vertical motion.

Time to Maximum Height

The time to reach maximum height in a vertical launch is the time required for the object’s upward velocity to reduce to zero under the influence of gravity. This time interval can be calculated by dividing the initial vertical velocity by the acceleration due to gravity, making it a central concept in solving problems related to vertical motion.

Transcript

0:00 All right.

00:01 So for this problem, we have a seed pod.

00:06 So some green dots, the seed pod.

00:09 And this seed pod is 20 centimeters above the ground.

00:14 So i'll draw the ground down here.

00:17 That's 20 centimeters below the seed pod.

00:20 And we're told that the seed pod is going to launch seeds 90 degrees vertically and 90 degrees vertically.

00:30 And 90 degrees, negative 90 degrees vertically.

00:35 So that's straight up and straight down.

00:41 And we need to find how much time passes before that seed that goes straight upwards reaches its maximum height.

00:53 So its trajectory will be up and then it will come to a stop and then start to fall back down until it hits the ground.

01:04 So we want to know how long does it take for it to reach that point? all right.

01:11 We're told that they have speeds ranging between 2 .3 and 4 .6 meters per second.

01:19 But we want to consider the case where it has its highest possible initial speed.

01:24 Okay.

01:25 The last thing we need to consider is what is its acceleration? we're told we can ignore air resistance.

01:31 So the only force acting then on the seed is gravity...

Please give Ace some feedback