A smoke jumper jumps from a plane that is 1800 ft above the ground. The function h=-16t^2+1800 gives the jumper's height h in feet during the free fall at t seconds.
a) the jumper is in free fall for blank seconds if the parachute opens at 1000 ft.
Round to two decimal places as needed!
b) the jumper is in free fall for blank seconds if the parachute opens at 940 ft.
Round to two decimal places as needed!
a) To find the time it takes for the jumper to be at a height of 1000 ft, we need to solve the equation h = -16t^2 + 1800 for t. Setting h to 1000, we get 1000 = -16t^2 + 1800. Rearranging this equation, we get -16t^2 = 1000 - 1800. Simplifying, we get -16t^2 = -800. Dividing both sides by -16, we get t^2 = 50. Taking the square root of both sides, we get t = sqrt(50) ≈ 7.07 seconds. Therefore, the jumper is in free fall for approximately 7.07 seconds if the parachute opens at 1000 ft.
b) To find the time it takes for the jumper to be at a height of 940 ft, we need to solve the equation h = -16t^2 + 1800 for t. Setting h to 940, we get 940 = -16t^2 + 1800. Rearranging this equation, we get -16t^2 = 940 - 1800. Simplifying, we get -16t^2 = -860. Dividing both sides by -16, we get t^2 = 53.75. Taking the square root of both sides, we get t = sqrt(53.75) ≈ 7.34 seconds. Therefore, the jumper is in free fall for approximately 7.34 seconds if the parachute opens at 940 ft.