A girl is standing at the edge of a cliff 100 . m above the ground. She reaches out over the edg

step 1 we have problem number 88 which is which is related to motion in a straight line motion in a str

A girl is standing at the edge of a cliff 100 . m above the...

A girl is standing at the edge of a cliff $100 . \mathrm{m}$ above the ground. She reaches out over the edge of the cliff and throws a rock straight upward with a speed $8.00 \mathrm{~m} / \mathrm{s}$. a) How long does it take the rock to hit the ground? b) What is the speed of the rock the instant before it hits the ground?

A girl is standing at the edge of a cliff $100 . \mathrm{m}$ above the ground. She reaches out over the edge of the cliff and throws a rock straight upward with a speed $8.00 \mathrm{~m} / \mathrm{s}$.
a) How long does it take the rock to hit the ground?
b) What is the speed of the rock the instant before it hits the ground?

Key Concepts

Kinematics Equations

These are the mathematical formulas that describe the motion of an object under constant acceleration. In problems like these, one often uses the displacement equation (s = s0 + v0*t + (1/2)*a*t^2) and the velocity equation (v = v0 + a*t) to determine characteristics such as time of flight and final velocity. These equations allow for systematic problem-solving when acceleration remains constant.

Gravitational Acceleration

This concept refers to the constant acceleration experienced by objects due to the gravitational pull of the Earth, which is approximately 9.8 m/s² downward. In kinematics problems, gravitational acceleration is a key factor in determining how fast an object falls and is integral to the equations of motion when dealing with free-falling bodies.

Projectile Motion

Projectile motion involves objects that are thrown or projected into the air, subject only to gravitational acceleration. It typically considers the vertical and horizontal components of motion separately. In vertical motion problems, like a rock thrown upward from an elevated position, the analysis focuses on how gravity affects the motion throughout its ascent and descent.

Quadratic Equations

When applying the kinematics equations to problems involving vertical motion, one often ends up with a quadratic equation in terms of time. Solving this quadratic equation is essential to find the time of flight or other time-dependent characteristics of the motion. The quadratic formula provides a systematic way to solve these second-order equations and identify the physically relevant solutions.

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