A stone is dropped from the edge of a roof, and hits the ground with a velocity of 100 feet per...

Question:

A stone is dropped from the edge of a roof, and hits the ground with a velocity of 100 feet per second. How high is the roof?

Kinematic Equation of Motion:

The kinematic equation of motion is used to describe the motion of the objects (under the effect of gravity) without considering the external or internal forces applied to the objects. The kinematic equation of third law is used to relate the travelled distance or height and velocity (final and initial velocities).

Answer and Explanation: 1


Given Data

  • The final velocity of the stone is: {eq}v = 100\;{\rm{ft/s}} {/eq}


The expression for the third kinematic equation of motion is,

{eq}{v^2} = {u^2} + 2gh {/eq}


Here, the initial velocity of the stone is u and the height of the roof is h.

The initial velocity is zero because the stone is dropped so {eq}u = 0 {/eq}.


Substitute the known values.

{eq}\begin{align*} {\left( {100\;{\rm{ft/s}}} \right)^2} &= {\left( 0 \right)^2} + 2\left( {32.2\;{\rm{ft/}}{{\rm{s}}^2}} \right)h\\ h &= \dfrac{{{{\left( {100\;{\rm{ft/s}}} \right)}^2}}}{{2\left( {32.2\;{\rm{ft/}}{{\rm{s}}^2}} \right)}}\\ h &= 155.279\;{\rm{ft}} \end{align*} {/eq}


Thus, the height of the roof is {eq}155.279\;{\rm{ft}} {/eq}.


Learn more about this topic:

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Practice Calculating Motion Using Kinematic Equations & Graphs

from

Chapter 3 / Lesson 18
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In kinematics, motion is understood through equations and graphs. Review sample problems and practice calculating motion with the various equations from the 'kinematics toolbox.'


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