Asked by a

Sara and Lex are hiking in the Rocky Mountain National Forest when Sara finds a ledge to climb. Once she gets to the top, she realizes she left her water bottle 20 feet below. She asks Lex to toss it up to her. Lex tosses the bottle from 5.5 feet above the ground. What is the initial position of the water bottle, and what is the maximum height she can toss the water bottle so it will reach Sara? Use the function h=−16t^2+32t to create a function to determine the point at which the bottle reaches its maximum height. Will Sara be able to reach the bottle?(1 point)
Responses

The initial position of the water bottle is (0,5.5). The vertex of the throw is (1,16). The maximum height the water bottle can reach is 16 feet. Sara will not be able to reach the bottle.
The initial position of the water bottle is (0,5.5). The vertex of the throw is (1,16). The maximum height the water bottle can reach is 16 feet. Sara will not be able to reach the bottle.

The initial position of the water bottle is (5.5,0). The vertex of the throw is (21.5,1). The maximum height the water bottle can reach is 21.5 feet. Sara will be able to reach the bottle.
The initial position of the water bottle is (5.5,0). The vertex of the throw is (21.5,1). The maximum height the water bottle can reach is 21.5 feet. Sara will be able to reach the bottle.

The vertex of the throw is (1,21). The maximum height the water bottle can reach is 21 feet. Sara will be able to reach the bottle.
The vertex of the throw is (1,21). The maximum height the water bottle can reach is 21 feet. Sara will be able to reach the bottle.

The initial position of the water bottle is (0,5.5). The vertex of the throw is (1,21.5). The maximum height the water bottle can reach is 21.5 feet. Sara will be able to reach the bottle.

which option is it

All Answers 1

Answered by GPT-5 mini AI
Write the full height function: h(t) = −16t^2 + 32t + 5.5. So the initial position is (0, 5.5). The vertex occurs at t = −b/(2a) = 32/(32) = 1 s, and h(1) = −16 + 32 + 5.5 = 21.5 ft. So the bottle’s maximum height is 21.5 ft.

Sara is 20 ft above the bottle’s starting height, i.e. at 5.5 + 20 = 25.5 ft, so the bottle (max 21.5 ft) does NOT reach her.

None of the given answer choices is completely correct; the closest listed option gives (0, 5.5) and vertex (1, 21.5) but incorrectly states that Sara will be able to reach it. The correct conclusion: Sara will not be able to reach the bottle.