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**Problem**: A hoodlum throws a stone vertically downward with an initial speed of 12.0m/s from the roof of a building, 30.0m above the ground. (a) How long does it take the stone to reach the ground? (b) What is the speed of the stone at impact?

###### FREE Expert Solution

###### FREE Expert Solution

We're asked for the *time of flight* and *final velocity* of the vertically-thrown stone.

Whenever we have a problem where an object is dropped or thrown from some height, it is affected only by the constant acceleration of gravity (*g* = 9.8 m/s) after being released, and therefore we can use the kinematics (UAM) equations. Because the motion is in the vertical direction, we'll replace Δ*x* with Δ*y*. Our standard coordinate system has the +*y*-axis pointing upwards, so we say *a *= −*g* = −9.8 m/s^{2}. To solve, we'll follow these steps:

- Identify the
for each part of the problem.__target variable__ - Identify
__which variables are__—remember that__known__*only*(Δ**3**of the**5**variables*y*,*v*_{0},*v*,_{f}*a*, and*t*)*are needed*to solve any kinematics problem, and we already know what*a*is. __Choose a UAM equation__with**only one unknown**, which should be our**target variable**.__Solve the equation__for the target variable, then__substitute known values__and__calculate__the answer.

$\overline{)\mathbf{}{{\mathit{v}}}_{{\mathit{f}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{-}}{\mathit{g}}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{y}}{\mathbf{=}}{\mathbf{}}\mathbf{\left(}\frac{{\mathit{v}}_{\mathit{f}}\mathbf{+}{\mathit{v}}_{\mathbf{0}}}{\mathbf{2}}\mathbf{\right)}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{y}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathit{t}}{\mathbf{-}}{\frac{1}{2}}{\mathit{g}}{{\mathit{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{\mathbf{}}{{{\mathit{v}}}_{{\mathit{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{\mathbf{}}{{{\mathit{v}}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{}}{\mathbf{-}}{\mathbf{2}}{\mathit{g}}{\mathbf{\u2206}}{\mathit{y}}}$

Remember that **down** is the *−y*-direction, and __make sure you're using the right sign__ for any velocities and displacements in the problem!

###### Problem Details

A hoodlum throws a stone vertically downward with an initial speed of 12.0m/s from the roof of a building, 30.0m above the ground.** ****(a)** How long does it take the stone to reach the ground? **(b)** What is the speed of the stone at impact?

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Vertical Motion and Free Fall concept. You can view video lessons to learn Vertical Motion and Free Fall Or if you need more Vertical Motion and Free Fall practice, you can also practice Vertical Motion and Free Fall practice problems .

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Based on our data, we think this problem is relevant for Professor Jerousek's class at UCF.

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