A stone is thrown vertically up from the edge of a cliff 35.0 m from the ground. The initial vel

step 1 In this question it is given that a stone is thrown vertically up from the edge of a cliff that

A stone is thrown vertically up from the edge of a cliff...

A stone is thrown vertically up from the edge of a cliff $35.0 \mathrm{m}$ from the ground. The initial velocity of the stone is $8.00 \mathrm{m} \mathrm{s}^{-1} .$ (See Figure $2.39 .)$ (a) How high will the stone get? (b) When will it hit the ground? (c) What velocity will it have just before hitting the ground? (d) What distance will the stone have covered? (e) What is the average speed and average velocity for this motion? (f) Make a graph to show the variation of velocity with time. (g) Make a graph to show the variation of displacement with time. (Take the acceleration due to gravity to be $\left.10.0 \mathrm{m} \mathrm{s}^{-2} .\right)$

A stone is thrown vertically up from the edge of a cliff $35.0 \mathrm{m}$ from the ground. The initial velocity of the stone is $8.00 \mathrm{m} \mathrm{s}^{-1} .$ (See Figure $2.39 .)$
(a) How high will the stone get?
(b) When will it hit the ground?
(c) What velocity will it have just before hitting the ground?
(d) What distance will the stone have covered?
(e) What is the average speed and average velocity for this motion?
(f) Make a graph to show the variation of velocity with time.
(g) Make a graph to show the variation of displacement with time.
(Take the acceleration due to gravity to be $\left.10.0 \mathrm{m} \mathrm{s}^{-2} .\right)$

Key Concepts

Graphical Representation of Motion

Graphing variables like velocity and displacement against time provides a visual understanding of the motion. A velocity-time graph illustrates how velocity changes (linearly for constant acceleration), with its slope representing acceleration, while a displacement-time graph shows how position changes with time, often revealing curvature that indicates acceleration effects.

Kinematic Equations

These are the formulas that relate displacement, initial velocity, time, acceleration, and final velocity for objects moving with constant acceleration. They form the mathematical backbone for solving problems in classical mechanics involving uniformly accelerated motion, such as calculating ranges, times, and velocities.

Vertical Projectile Motion

This concept describes the motion of objects thrown vertically, where the only constant acceleration is due to gravity. It involves upward motion that decelerates until the object stops momentarily at its highest point, then accelerates downward, obeying the symmetry properties of motion under constant acceleration.

Time of Flight and Maximum Height

These are analyses specific to vertical motion where time of flight is the total time an object spends in the air and maximum height is the peak altitude reached. Calculating these requires understanding the interplay between initial velocity and gravitational acceleration, applying kinematic equations appropriately for different phases of the motion.

Displacement vs. Distance

Displacement is the vector quantity representing the change in position of an object, taking into account direction, whereas distance is the scalar quantity that measures the total path length traveled regardless of direction. Distinguishing the two is critical in understanding motion, as they can yield different values in situations involving changes in the direction of movement.

Average Speed vs. Average Velocity

Average speed is defined as the total distance traveled divided by the total time taken, while average velocity is the displacement divided by the time interval. This distinction is important especially in non-linear motions, where the path traveled and overall change in position differ, resulting in different numerical values for these averages.

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