A very strong, but inept, shot putter puts the shot straight...

A very strong, but inept, shot putter puts the shot straight up vertically with an initial velocity of $11.0 \mathrm{m} / \mathrm{s}$.
How long a time does he have to get out of the way if the shot was released at a height of $2.20 \mathrm{m}$ and he is $1.80 \mathrm{m}$ tall?

Key Concepts

Constant Acceleration (Gravity)

Gravity provides a uniform acceleration for all objects near the surface of the Earth, usually approximated as 9.8 m/s² downward. This constant acceleration is a key input in the kinematic equations when analyzing motions such as a shot thrown vertically upward, as it influences both the ascent and descent of the object.

Quadratic Equations in Motion

When solving for the time at which an object reaches a particular position in uniformly accelerated motion, the kinematic equations often lead to quadratic equations in time. Solving these quadratics allows one to determine the specific time values at which the object will be at a given height, which is crucial for timing and safety assessments in practical applications.

Kinematics Equations

Kinematics equations describe the motion of objects under constant acceleration. These equations, such as s = ut + ½at² and v = u + at, allow us to relate displacement, initial velocity, time, acceleration, and final velocity, which are essential for analyzing problems involving objects moving under gravity.

Projectile Motion

Projectile motion addresses the trajectory of an object that is projected into the air and moves under the influence of gravity alone, typically ignoring air resistance. In vertical motion problems, these principles help determine the time taken to reach specific heights and when the object will land, by treating the vertical motion as a one-dimensional problem with constant acceleration.

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