Question

question 22 (5 points) a gust of wind forces a rock to fall off a cliff thats 20 feet high. this is represented by the function h(t)=-16t² + 20, where t represents the time measured in seconds, and h represents height above the ground. approximate how many seconds it takes for the rock to hit the ground, to two decimal places. 1.00 seconds 1.12 seconds 1.25 seconds 1.50 seconds

Explanation:

Step1: Set height h(t) to 0

When the rock hits the ground, its height above the ground is 0. So we set the function $h(t)=- 16t^{2}+20 = 0$.

Step2: Solve for t

First, rewrite the equation as $16t^{2}=20$. Then $t^{2}=\frac{20}{16}=\frac{5}{4}$. Taking the square - root of both sides, we get $t=\pm\sqrt{\frac{5}{4}}$. Since time cannot be negative in this context, we only consider the positive value. So $t = \sqrt{\frac{5}{4}}=\frac{\sqrt{5}}{2}\approx1.12$ seconds.

Answer:

1.12 seconds