Question

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?
$h(t) = at^2 + vt + h_0$
2.4 s
40.7 s
9.7 s
1.9 s

Explanation:

Step1: Identify given values

We know \( a = -16 \, \text{ft/s}^2 \), \( v = 0 \, \text{ft/s} \), \( h_0 = 90 \, \text{ft} \), and when the egg reaches the ground, \( h(t) = 0 \). The height function is \( h(t)=at^2 + vt+h_0 \).

Step2: Substitute values into the function

Substitute the known values into the height function: \( 0=-16t^2 + 0\times t+90 \), which simplifies to \( 16t^2=90 \).

Step3: Solve for \( t \)

First, divide both sides by 16: \( t^2=\frac{90}{16}=\frac{45}{8} = 5.625 \). Then take the square root of both sides. Since time cannot be negative, we consider the positive root: \( t=\sqrt{5.625}\approx2.4 \, \text{s} \).

Answer:

2.4 s