Question

a smoke jumper jumps from a plane that is 1900 ft above the ground. the function $h = -16t^2 + 1900$ gives the jumpers height $h$ in feet during the free fall at $t$ seconds

a. how long is the jumper in free fall if the parachute opens at 1000 ft?
b. how long is the jumper in free fall if the parachute opens at 940 ft?
c. what is a reasonable domain and range for the function $h?$

a. the jumper is in free fall for 7.50 s if the parachute opens at 1000 ft.
(round to two decimal places as needed.)
b. the jumper is in free fall for \\(\square\\) s if the parachute opens at 940 ft.
(round to two decimal places as needed.)

Explanation:

Step1: Set up the equation

We know the height function is \( h = -16t^2 + 1900 \). When the parachute opens at \( h = 940 \) ft, we set up the equation \( 940=-16t^2 + 1900 \).

Step2: Solve for \( t^2 \)

First, subtract 1900 from both sides: \( 940 - 1900=-16t^2 \), which simplifies to \( - 960=-16t^2 \). Then divide both sides by - 16: \( t^2=\frac{-960}{-16} = 60 \).

Step3: Solve for \( t \)

Take the square root of both sides. Since time \( t\geq0 \), we have \( t=\sqrt{60}\approx7.75 \) (rounded to two decimal places).

Answer:

\( 7.75 \)