Answer to Question #266785 in Mechanics | Relativity for JINGJING

Question

 FA8: A plumb bob is dropped from the top of a 30.0 –ft building. Find: 

a. how long will it take the object to hit the ground?

 b. at what velocity will it hit the ground?

 c. how many meters shall have it fallen to have a velocity of 2.75 m/s?

 d. how many seconds shall have it fallen to travel 8.0 m?

 e. its displacement after 7.0 s

 f. how many seconds of its fall will it attain a velocity of 5.0 m/s

Answer 1

Solution.

$h=30ft=9.144m;$

$a) h=\dfrac{gt^2}{2}\implies t=\sqrt{\dfrac{2h}{g}};$

$t=\sqrt{\dfrac{2\sdot9.144}{9.8}}=1.135s;$

$b) v=gt;$

$v=9.8\sdot1.135=11.122 m/s;$

$c)v=2.75 m/s$; $l=\dfrac{v^2}{2g};$

$l=\dfrac{2.75^2}{2\sdot9.8}=0.386 m;$

$d)l=8 m; l=\dfrac{gt^2}{2}\implies t=\sqrt{\dfrac{2l}{g}};$

$t=\sqrt{\dfrac{2\sdot8}{9.8}}=1.633s;$

$e) t=7s; S=h=9.144 m;$

$f) v=5 m/s;$ $v=gt\implies t=\dfrac{v}{g};$

$t=\dfrac{5}{9.8}=0.51s;$

Answer: $a) t=1.135s;$

$b)v=11.122 m/s;$

$c) l=0.386m;$

$d) t=1.633 s;$

$e)S=9.144 m;$

$f) t=0.51s.$