Question

To determine the height of a tall building such as Sears Tower in Chicago, Illinois a ball was dropped from the top of the building to the ground. If the time was measured to be 9.5 s. Find height of Sears Tower in feet. (Use 1 foot = 0.305 m).

Answer 1

Answer:

The height of Sears Tower is 1448.5 feet.

Explanation:

We apply the free fall formula to the ball:

$y=v_{o} *t+\frac{1}{2} *g*t^{2}$

y: The vertical distance the ball moves at time t  

$v_{o}$i: Initial speed

g=Gravity acceleration=$9.8*(\frac{\frac{1ft}{0.305m} }{s^{2} } )$

Known information

We know that the vertical distance (y) that the ball moves in 9,5s  is equal to height of Sears Tower (h).  

Too we know that the ball is released from rest, then,$v_{0}$=0

Height of Sears Tower calculation:

We replace  in the equation 1 the data following;

$y=h$

$v_{o} =0$

$g=32,1\frac{ft}{s^{2} }$

$t= 9,5s$

$h=0*9.5+\frac{1}{2} *32.1*9.5^{2}$

$h=1448.5 ft$

Answer: The height of Sears Tower is 1448.5 ft