an egg is dropped from a height of 90 ft. if acceleration due to gravity is -16 ft/s² and initial velocity…

an egg is dropped from a height of 90 ft. if acceleration due to gravity is -16 ft/s² and initial velocity is 0 ft/s, approximately how long will it take for the egg to reach the ground?\nh(t)=at² + vt+h₀\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/s² and initial velocity is 0 ft/s, approximately how long will it take for the egg to reach the ground?\nh(t)=at² + vt+h₀\n1.9 s\n2.4 s\n9.7 s\n40.7 s

Answer

Explanation:

Step1: Identify the values

Given $a=- 16$, $v = 0$, $h_0=90$, and $h(t)=0$ (when the egg reaches the ground). Substitute into the formula $h(t)=at^{2}+vt + h_0$. $0=-16t^{2}+0\times t + 90$

Step2: Solve for $t$

We have the equation $-16t^{2}+90 = 0$. Rearrange it to get $16t^{2}=90$. Then $t^{2}=\frac{90}{16}=\frac{45}{8}$. Take the square - root of both sides: $t=\sqrt{\frac{45}{8}}\approx\sqrt{5.625}\approx2.4$.

Answer:

2.4 s