Question

the height of a stuntperson jumping off a building that is 20 m high is modeled by the equation h = 20 - 5t², where t is the time in seconds. a high - speed camera is ready to film the person between 15 m and 10 m above the ground. for which interval of time should the camera film the person?
o t = √2
o 1 < t < √2
o t > √2
o 1 < t < 2

Explanation:

Step1: Set up the inequality

We want to find \(t\) such that \(10\leq20 - 5t^{2}\leq15\).
First, solve the left - hand side of the inequality \(10\leq20 - 5t^{2}\):

$$
LATEXBLOCK0
$$

Since \(t\geq0\) (time cannot be negative), we have \(0\leq t\leq\sqrt{2}\).
Next, solve the right - hand side of the inequality \(20 - 5t^{2}\leq15\):

$$
LATEXBLOCK1
$$

Since \(t\geq0\), we have \(t\geq1\).

Step2: Find the intersection of the two solution sets

The intersection of \(0\leq t\leq\sqrt{2}\) and \(t\geq1\) is \(1\leq t\leq\sqrt{2}\).

Answer:

\(1\leq t\leq\sqrt{2}\)