{"id":"cb_practice_pdf:t7-math-m2-q19","source_id":"cb_practice_pdf","source_item_id":"t7-math-m2-q19","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":null,"form_id":"cb_practice_pdf:test-7","module_number":2,"position":19,"stem":"h ( t) = −16t^2 +b The function h estimates an object’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 = 0 ground when it is dropped at t. Approximately how many seconds after being dropped does the function estimate the object will hit the ground?","stimulus":"","stimulus_html":null,"stem_html":"<p>h ( t) = −16t^2 +b The function h estimates an object’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 = 0 ground when it is dropped at t. Approximately how many seconds after being dropped does the function estimate the object will hit the ground?</p>","rationale_html":"<p>Choice B is correct. It’s given that the function h estimates that the object is 3,364 = 3,364 feet above the ground when it’s dropped at t 0. Substituting for 3,364=-16 0 2+ 3,364= h^th and 0 for t in the function h yields ^ h b, or b. 3,364 =-16 2+3,364 Substituting for b in the function h yields h^th t . When the object hits the ground, its height will be 0 feet above the ground. Substituting 0 =-16 2+3,364 0=-16 2+3,364 16 2 for h^th in h^th t yields t . Adding t to each 16 2=3,364 16 side of this equation yields t . Dividing each side of this equation by 2=210.25 yields t . 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 =14.50 square root of each side of this equation, which yields t . It follows that the 14.50 function estimates the object will hit the ground approximately seconds after being dropped. 7.25 Choice A is incorrect. The function estimates that seconds after being -16 7.25 2+3,364 2,523 dropped, the object’s height will be ^ h feet, or 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. 43 SAT PRACTICE TEST #7 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2</p>","correct_answer":["B"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>7.25</p>","ord":0},{"label":"B","content_html":"<p>14.50</p>","ord":1},{"label":"C","content_html":"<p>105.13</p>","ord":2},{"label":"D","content_html":"<p>210.25</p>","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}