Luther and Thor are hiking in the National Forest when Luther finds a ledge to climb. Once he gets to the top, he realizes he left her water bottle 20 feet below. He asks Luther to toss it up to he. Thor 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 he can toss the water bottle so it will reach Luther? Use the function h=−16t^2+32t to create a function to determine the point at which the bottle reaches its maximum height. Will Luther be able to reach the bottle.
To determine the initial position of the water bottle, we can assume that Thor throws the bottle at time t=0. Since Thor is 5.5 feet above the ground, the initial position of the water bottle is 5.5 feet above the ground.
To find the maximum height the bottle can reach, we need to find the vertex of the quadratic function h=-16t^2+32t. The vertex of a quadratic function with the form h = at^2 + bt + c is given by the x-coordinate of the vertex, which is given by the formula x = -b/(2a). In this case, a=-16 and b=32, so the x-coordinate of the vertex is -32/(2*-16) = 1.
To find the corresponding y-coordinate (maximum height), we substitute t=1 into the equation h=-16t^2+32t: h = -16(1)^2 + 32(1) = 16 feet.
Therefore, the maximum height the bottle can reach is 16 feet.
Since the initial position of the water bottle is 5.5 feet above the ground and the maximum height is 16 feet, Luther will be able to reach the bottle since it will be above his location on the ledge.
Luther and Thor are hiking in the National Forest when Luther finds a ledge to climb. Once he gets to the top, he realizes he left his water bottle 20 feet below. He asks Thor to toss it up to he. Thor 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 he can toss the water bottle so it will reach Luther? Use the function h=−16t^2+32t to create a function to determine the point at which the bottle reaches its maximum height. Will Luther be able to reach the bottle.
To determine the initial position of the water bottle, we can assume that Thor throws the bottle at time t=0. Since Thor is 5.5 feet above the ground, the initial position of the water bottle is 5.5 feet above the ground.
Now, let's find the time it takes for the bottle to reach its maximum height. The function h=-16t^2+32t represents the height of the bottle in terms of time t. To find the time at which the bottle reaches its maximum height, we need to find the vertex of this quadratic function. The x-coordinate of the vertex is given by -b/(2a), where a=-16 and b=32 in this case. Thus, the time at which the bottle reaches its maximum height is t=-b/(2a)=-32/(2*-16) = 1.
To find the maximum height, we substitute t=1 back into the function h=-16t^2+32t: h=-16(1)^2+32(1) = 16 feet.
Therefore, the maximum height the bottle can reach is 16 feet.
Since the initial position of the water bottle is 5.5 feet above the ground, which is lower than the maximum height of 16 feet, Luther will be able to reach the bottle.
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=−16t2+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?
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 (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 (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.
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 open paren 0 comma 5 point 5 close paren. The vertex of the throw is left parenthesis 1 comma 16 right parenthesis . The maximum height the water bottle can reach is 16 feet. Sara will not be able to reach the bottle.