Answer to Question #109823 in Algebra for Kay

Question

On July 28, 1945, an airplane crashed into the 78th and 79th floors of the Empire State Building in New York City. Hundreds of pieces of debris fell 975 feet to the street below.

a) How long did it take for the debris to reach the ground? Use the formula
h = -16t2 + 975.


b) How much time after hearing the crash did the people on the street have to get out of the way of the falling debris? (sound travels at about 1100ft/sec.)
Please help I have been doing this for a solid 3 hours

Answer 1

(a) Let's calculate t₀ = time when debris reach the ground.

$h=-16t^2+975\\When\;debris\;reach\;the\;ground,\;h=0.\\0=-16t_0^2+975\\t_0^2=\frac{975}{16}\Rightarrow t_0=\sqrt{\frac{975}{16}}\Rightarrow t_0\approx7.806s\\$

(b) Let's calculate t₁ = time when people on the street hear the crash.

So, answer will be t₀-t₁ = time people have to get out of the way after hearing before debris fall.

$t_0\approx7.806sec\\t_1=\frac{975ft}{1100ft/s}\approx0.886s\\t_0-t_1=7.806s-0.886s\;=\;6.92s$

Answer: (a) 7.806s (b) 6.92s