an egg is dropped from a height of 90 ft. if acceleration due to gravity is $-16$ ft/s$^2$ and initial…

an egg is dropped from a height of 90 ft. if acceleration due to gravity is $-16$ ft/s$^2$ and initial velocity is 0 ft/s, approximately how long will it take for the egg to reach the ground?\n$h(t) = at^2 + vt + h_0$\n1.9 s\n2.4 s\n9.7 s\n40.7 s

an egg is dropped from a height of 90 ft. if acceleration due to gravity is $-16$ ft/s$^2$ and initial velocity is 0 ft/s, approximately how long will it take for the egg to reach the ground?\n$h(t) = at^2 + vt + h_0$\n1.9 s\n2.4 s\n9.7 s\n40.7 s

Answer

Explanation:

Step1: Substitute known values

Substitute $a=-16$, $v=0$, $h(t)=0$, $h_0=90$ into $h(t)=at^2+vt+h_0$: $0 = -16t^2 + 0 \cdot t + 90$ Simplify to: $-16t^2 + 90 = 0$

Step2: Isolate the $t^2$ term

Rearrange to solve for $t^2$: $16t^2 = 90$ $t^2 = \frac{90}{16}$

Step3: Calculate $t$

Take positive square root (time can't be negative): $t = \sqrt{\frac{90}{16}} = \frac{\sqrt{90}}{4} = \frac{3\sqrt{10}}{4} \approx 2.4$

Answer:

B. 2.4 s