Question

A ball is dropped from a treetop 256 feet above the ground. How long does it take to hit the ground? (s = 16t2)

Answer 1

Hence the ball would take about 4 seconds to hit the ground, so the answer is (A). 

Answer 2

Answer:

$t=4s$

Step-by-step explanation:

The vertical displacement of an object in freefall is given by the next equation:

$\Delta y=y_f-y_i=v_o_y t-\frac{1}{2} gt^2$

Where:

$y_f=Final\hspace{3}position\\y_i=Initial\hspace{3}position\\t=Time\\g=Standard\hspace{3}gravity\\v_o_y=Initial\hspace{3}velocity\hspace{3}in\hspace{3}y-axis$

This equation can be reduced to the equation given by the problem since:

$v_o_y=0\\y_f=0\\y_i=s=256\\g\approx 32ft/s^2$

Hence:

$-s=-\frac{1}{2} 32t^2$

Solving for t:

$t^2=\frac{256}{16} =16\\\\t=\sqrt{16} =\pm4s$

Since a negative time wouldn't have sense, the answer is 4 seconds