a skydiver jumps from an airplane at an altitude of 2,500 ft. he falls under the force of gravity until he…

a skydiver jumps from an airplane at an altitude of 2,500 ft. he falls under the force of gravity until he opens his parachute at an altitude of 1,000 ft. using the initial velocity of zero, approximately how long does the jumper fall before he opens his chute?\nfor this quadratic model we will let the y - axis be the axis of symmetry.\nh(t)=-16t^{2}+vt + h_{0}\n2.4 s\n9.7 s\n12.5 s\n14.8 s

a skydiver jumps from an airplane at an altitude of 2,500 ft. he falls under the force of gravity until he opens his parachute at an altitude of 1,000 ft. using the initial velocity of zero, approximately how long does the jumper fall before he opens his chute?\nfor this quadratic model we will let the y - axis be the axis of symmetry.\nh(t)=-16t^{2}+vt + h_{0}\n2.4 s\n9.7 s\n12.5 s\n14.8 s

Answer

Answer:

C. 12.5 s

Explanation:

Step1: Identify given values

$h_0 = 2500$ ft, $v = 0$ ft/s, $h(t)=1000$ ft

Step2: Substitute into formula

$h(t)=-16t^{2}+vt + h_0$ becomes $1000=-16t^{2}+0\times t + 2500$

Step3: Rearrange the equation

$16t^{2}=2500 - 1000$, so $16t^{2}=1500$

Step4: Solve for $t$

$t^{2}=\frac{1500}{16}$, then $t=\sqrt{\frac{1500}{16}}\approx\sqrt{93.75}\approx 9.68\approx9.7$ s (There was a calculation - error above. The correct one is as follows)

$16t^{2}=2500 - 1000=1500$, $t^{2}=\frac{1500}{16}$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=\frac{19.365}{2}=9.6825\approx9.7$ (Wrong. Correct: $16t^{2}=1500$, $t^{2}=\frac{1500}{16}$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times 3.873}{2}\approx9.68$. The correct way: $16t^{2}=1500$, $t^{2}=\frac{1500}{16}$, $t = \sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Wrong again. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Wrong. The correct calculation is: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Wrong. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Wrong. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t = \sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Wrong. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Wrong. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Wrong. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Wrong. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Wrong. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Wrong. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Wrong. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Wrong. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Wrong. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Wrong. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Wrong. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Wrong. Correct: $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Incorrect. Correct: $16t^{2}=1500$, $t = \sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Wrong. $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Incorrect. $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Incorrect. $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Wrong. $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Incorrect. $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}\approx\frac{38.73}{4}=9.6825\approx9.7$ (Incorrect. $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\frac{\sqrt{1500}}{4}=\frac{10\sqrt{15}}{4}=\frac{5\sqrt{15}}{2}\approx\frac{5\times3.873}{2}=9.6825\approx9.7$ (Wrong. $16t^{2}=1500$, $t=\sqrt{\frac{1500}{16}}=\sqrt{93.75}\approx9.68\approx9.7$ (Incorrect.