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 In this problem of motion in a straight line we have given that a hot air balloon is ascending a

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 spced docs it hit the ground?

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Key Concepts

Uniformly Accelerated Motion

This concept involves motion where the acceleration is constant. In such situations, the kinematic equations can be used to relate displacement, initial velocity, acceleration, and time, which are essential in solving problems involving objects moving under gravity.

Gravitational Acceleration

Gravitational acceleration is the constant acceleration experienced by objects in free-fall near the Earth's surface, typically approximated as 9.8 m/s² downward. It is a crucial factor in determining the motion of falling objects.

Kinematic Equations

Kinematic equations provide the mathematical framework to analyze the motion of objects under uniform acceleration. They allow for solving various unknowns such as time of flight, final velocity, and displacement when the initial conditions and acceleration are known.

Quadratic Equations in Motion Analysis

When applying kinematic equations to problems with vertical motion, the resulting equations often take a quadratic form. Solving these quadratic equations using methods like the quadratic formula is key to determining values such as the time at which an object reaches the ground.

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