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 $t$\
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 $h$?\
(round to two decimal places as needed )\
c. what is a reasonable domain for the function $h$?\
\\(\bigcirc\\) a. $-1900 \leq t \leq 1900$\
\\(\bigcirc\\) b. $0 \leq t \leq 1900$\
\\(\bigcirc\\) c. $0 \leq t \leq 10$\
\\(\bigcirc\\) d. $-10 \leq t \leq 10$\
\\(\bigcirc\\) e. all real numbers\
what is a reasonable range for the function $h$?\
\\(\bigcirc\\) a. $0 \leq h \leq 1900$\
\\(\bigcirc\\) b. $-10 \leq h \leq 10$\
\\(\bigcirc\\) c. $-1900 \leq h \leq 1900$\
\\(\bigcirc\\) d. $0 \leq h \leq 10$\
\\(\bigcirc\\) e. all real numbers

Explanation:

For the domain of \( h = -16t^2 + 1900 \): Time \( t \) starts at 0 (when the jumper jumps) and ends when \( h = 0 \) (ground level). Solving \( 0=-16t^2 + 1900 \) gives \( t=\sqrt{\frac{1900}{16}}\approx10.91 \), so a reasonable domain is \( 0\leq t\leq10 \) (option C).

For the range: Height \( h \) starts at 1900 ft (when \( t = 0 \)) and decreases to 0 ft (ground level). So the range is \( 0\leq h\leq1900 \) (option A).

Answer:

Domain: C. \( 0\leq t\leq10 \)
Range: A. \( 0\leq h\leq1900 \)