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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

Verified Answer :

bigweed

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

carlos2112

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

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