Question

a smoke jumper jumps from a plane that is 1900 ft above the ground. the function $h = -16t^2 + 1900$ gives the jumper’s 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 \\(\square\\) s if the parachute opens at 1000 ft

(round to two decimal places as needed )

Explanation:

Step1: Set h = 1000 in the function

We know the height function is \( h = -16t^2 + 1900 \). When the parachute opens at 1000 ft, we set \( h = 1000 \), so the equation becomes \( 1000 = -16t^2 + 1900 \).

Step2: Solve for t

First, subtract 1900 from both sides: \( 1000 - 1900 = -16t^2 \), which simplifies to \( -900 = -16t^2 \). Then divide both sides by -16: \( t^2=\frac{900}{16}=\frac{225}{4} \). Take the square root of both sides (we consider the positive root since time can't be negative): \( t = \sqrt{\frac{225}{4}}=\frac{15}{2} = 7.50 \) (rounded to two decimal places).

Answer:

7.50