Question

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

4 seconds
8 seconds
16 seconds

Answer 1

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

Answer 2

`t=4s`

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-(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=-(1)/(2) 32t^2`

Solving for t:

`t^2=(256)/(16) =16\\\\t=√(16) =\pm4s`

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