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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.