A hot-air balloon is ascending at the rate of 12 m / s and is 80 m above the ground when a pac

step 1 Hot Air balloon has an initial velocity of 12 meters per second, positive 12, an initial height,

A hot-air balloon is ascending at the rate of 12 m / s and...

A hot-air balloon is ascending at the rate of $12 \mathrm{~m} / \mathrm{s}$ and is $80 \mathrm{~m}$ above the ground when a package is dropped over the side. (a) How long does the package take to reach the ground? (b) With what speed does it hit the ground?

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Key Concepts

Kinematics of Uniformly Accelerated Motion

This concept involves the use of equations that describe the motion of objects under a constant acceleration, such as gravity. These equations link displacement, velocity, acceleration, and time, and are fundamental to solving problems in mechanics where the acceleration does not change over time.

Free Fall Motion

Free fall refers to the motion of an object when gravity is the only force acting upon it. The acceleration due to gravity is constant and acts downward, and understanding this concept is key to analyzing objects dropped or thrown in a gravitational field.

Initial Conditions in Projectile Motion

When analyzing the motion of a projectile, it is crucial to account for the initial conditions, such as initial position and initial velocity. These initial values determine the subsequent motion of the object and affect outcomes like time of flight and impact speed.

Application of Quadratic Equations in Kinematics

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