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katen-ka-za [31]
3 years ago
12

A lead ball is dropped 30 feet from a church tower. If the acceleration due to gravity is 9.8m s^-2, how long does it take the b

all to fall to the ground?
Physics
1 answer:
Alika [10]3 years ago
4 0

<em>fina</em><em>l</em><em> </em><em>velo</em><em>city</em><em> </em><em>of</em><em> </em><em>a</em><em> </em><em>falli</em><em>ng</em><em> </em><em>obj</em><em>ect</em><em> </em><em>=</em><em> </em><em>0</em>

<em>and</em><em> </em><em>accel</em><em>eration</em><em> </em><em>of</em><em> </em><em>a</em><em> </em><em>falli</em><em>ng</em><em> object</em><em> </em><em>is</em><em> </em><em>nega</em><em>tive</em>

<em>now</em><em> </em><em>usi</em><em>ng</em><em> </em><em>the</em><em> </em><em>exp</em><em>ression</em><em> </em><em>(</em><em> </em><em>Newton's</em><em> </em><em>3</em><em>r</em><em>d</em><em> </em><em>eq</em><em>uation</em><em> </em><em>of</em><em> </em><em>mo</em><em>tion</em><em>)</em>

<em>{v}^{2}  =  {u}^{2}  - 2gs</em>

<em>wher</em><em>e</em><em> </em><em>the</em><em> </em><em>para</em><em>meters</em><em> </em><em>ha</em><em>ve</em><em> </em><em>the</em><em>ir</em><em> </em><em>usu</em><em>al</em><em> </em><em>meaning</em>

<em>maki</em><em>ng</em><em> </em>

<em>{u}^{2}  \: the \: subject</em>

<em>thus</em><em> </em>

<em>{u}^{2}  = 2gs</em>

<em>u =  \sqrt{2gs}</em>

<em>from</em><em> </em><em>the</em><em> </em><em>question</em><em>,</em><em> </em>

<em>g</em><em>=</em><em> </em><em>9</em><em>.</em><em>8</em><em>m</em><em>/</em><em>s^</em><em>2</em>

<em>s</em><em> </em><em>=</em><em> </em><em>3</em><em>0</em><em>m</em>

<em>sub</em><em>stitute</em><em> </em><em>the</em><em>m</em><em> </em><em>in</em><em>to</em><em> </em><em>th</em><em>e</em><em> equation</em>

<em>u =  \sqrt{2(9.8 \times 30)}</em>

<em>u =  \sqrt{588}</em>

<em>u</em><em> </em><em>=</em><em> </em><em>2</em><em>4</em><em>.</em><em>2</em><em>5</em><em>m</em><em>/</em><em>s</em>

<em>but</em><em> </em><em>the</em><em> </em><em>qu</em><em>estion</em><em> </em><em>is</em><em> </em><em>dem</em><em>anding</em><em> </em><em>for</em><em> </em><em>tim</em><em>e</em><em> </em><em>but</em><em> </em><em>no</em><em>t</em><em> </em><em>the</em><em> </em><em>ini</em><em>tial</em><em> </em><em>veloc</em><em>ity</em>

<em>so</em><em> </em><em>sub</em><em>stitute</em><em> </em><em>them</em><em> </em><em>in</em><em> </em><em>the</em>

<em>Newton's</em><em> first</em><em> </em><em>eq</em><em>uation</em><em> </em><em>of</em><em> </em><em>motion</em>

where

V = u - gt

but from the question,

v= 0 and the acceleration is negative because it's a free fall

substitute the values into the equation

0 = 24.24 -9.8t

making t the subject

9.8t = 22.24

dividing through by 9.8

9.8t/9.8 = 22.24/9.8

t = 2.3s . therefore, it would take 2.3s for the ball to hit the ground.

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