A balloon is at a height of 12.8 m above the ground and is ascending with a velocity of 12 m

step 1 Here we have been given x is equal to distance travel is equal to 12 .8 meters and the initial v

A balloon is at a height of 12.8 m above the ground and is...

A balloon is at a height of $12.8 \mathrm{~m}$ above the ground and is ascending with a velocity of $12 \mathrm{~m} \mathrm{~s}^{-1} .$ A $2 \mathrm{~kg}$ body is dropped from it. It will reach the ground in $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$ (a) $1.5 \mathrm{~s}$ (b) $2 \mathrm{~s}$ (c) $3.2 \mathrm{~s}$ (d) $4.5 \mathrm{~s}$

A balloon is at a height of $12.8 \mathrm{~m}$ above the ground and is ascending with a velocity of $12 \mathrm{~m} \mathrm{~s}^{-1} .$ A $2 \mathrm{~kg}$ body is dropped from it. It will reach the ground in $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $1.5 \mathrm{~s}$
(b) $2 \mathrm{~s}$
(c) $3.2 \mathrm{~s}$
(d) $4.5 \mathrm{~s}$

Key Concepts

Uniformly Accelerated Motion

This concept refers to motion in which the acceleration is constant over time. In problems involving gravity, such as free-fall or vertical motion, the acceleration due to gravity is typically constant. The kinematic equations derived from this principle enable us to relate displacement, initial velocity, time, and acceleration, forming the core method for solving such dynamics problems.

Initial Conditions in Kinematics

In any motion analysis, determining the initial conditions—such as the initial height and the initial velocity—is crucial. These parameters set the starting point for solving kinematic equations and thereby influence the subsequent evolution of the system's motion, whether the object is moving upward or downward at the time of release.

Projectile Motion

Though not all projectile motion problems involve a horizontal component, vertical motion under gravity forms a subcategory of projectile motion. Understanding how an object moves when it is projected upward or downward involves analyzing its vertical displacement under the influence of constant gravitational acceleration, combining initial velocity and height to determine outcomes like time of flight.

Solving Quadratic Equations in Kinematics

When applying kinematic equations to scenarios where displacement depends on time squared, the resulting equations are quadratic in nature. Solving these equations accurately is essential in finding correct time intervals or distances, and often requires selecting the physically meaningful solution from the mathematical roots obtained.

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