Repeat Prob. 2 / 57 for the case where aerodynamic drag is...

Repeat Prob. $2 / 57$ for the case where aerodynamic drag is included. The magnitude of the drag deceleration is $k v^{2},$ where $k=3.5\left(10^{-3}\right) \mathrm{ft}^{-1}$ and $v$ is the speed in feet per second. The direction of the drag is opposite the motion of the projectile throughout the flight (when the projectile is moving upward, the drag is directed downward, and when the projectile is moving downward, the drag is directed upward).

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

Deceleration

Deceleration refers to the reduction of speed due to resistive forces like aerodynamic drag. In the context of projectile motion, drag causes the object to slow down by exerting a force opposite to the direction of motion, affecting both the upward and downward phases of its flight.

Differential Equations

Differential equations are used to model the motion of projectiles under forces such as gravity and air resistance. When drag is included, the equations of motion become non-linear and may require numerical methods for their solution. These equations provide the relationship between the object's velocity, acceleration, and time.

Projectile Motion

Projectile motion refers to the motion of an object that is launched into the air and influenced only by gravity and possibly other forces like aerodynamic drag. In a typical analysis, the motion is broken into horizontal and vertical components, and the object's trajectory is determined by solving the corresponding equations of motion.

Aerodynamic Drag

Aerodynamic drag is a force exerted by a fluid (such as air) that opposes the motion of an object. It typically depends on the object's speed and shape. In many problems, the drag force is modeled as being proportional to the square of the speed, which creates a non-linear resistive effect on the object's motion.

Transcript

Please give Ace some feedback