OG详解-OG7 数学2 Q19

Choice B is correct. It’s given that the function h estimates that the object is 3,364 feet above the ground when it’s dropped at t = 0. Substituting 3,364 for h(t) and 0 for t in the function h yields 3,364 =-16(0)² +b, or 3,364 = b. Substituting 3,364 for b in the function h yields h(t)=-16t² +3,364. When the object hits the ground, its height will be 0 feet above the ground. Substituting 0 for h(t) in h(t)=-16t² +3,364 yields 0 =-16t² +3,364. Adding 16t²  to each side of this equation yields 16t² = 3,364. Dividing each side of this equation by 16 yields t² = 210.25. Since the object will hit the ground at a positive number of seconds after it’s dropped, the value of t can be found by taking the positive square root of each side of this equation, which yields t = 14.50. It follows that the function estimates the object will hit the ground approximately 14.50 seconds after being dropped.
Choice A is incorrect. The function estimates that 7.25 seconds after being dropped, the object’s height will be -16(7.25)² +3,364 feet, or 2,523 feet, above the ground. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.