h t = - 16 t 2 + b The function h estimates an object’s height, in feet, above the

Question

h t = - 16 t 2 + b The function h estimates an object&rsquo;s height, in feet, above the ground t seconds after the object is dropped, where b is a constant. The function estimates that the object is 3,364 feet above the ground when it is dropped at t = 0 . Approximately how many seconds after being dropped does the function estimate the object will hit the ground?

Accepted Answer

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 = - 16 t 2 + 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 = - 16 t 2 + 3,364 yields 0 = - 16 t 2 + 3,364 . Adding 16 t 2 to each side of this equation yields 16 t 2 = 3,364 . Dividing each side of this equation by 16 yields t 2 = 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.

Question h-t-16