Question
A stunt driver for the Duke of Hazzard drove the General Lee off a ramp and landed on the ground a few seconds later. His height in feet is given by h=-16t^2+16t+50 where t is the time in seconds.
What was the height of the ramp?
What was the maximum height achieved?
What was the height of the ramp?
What was the maximum height achieved?
Answers
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Answered by
GPT 3.5
To find the height of the ramp, we need to determine the height when the time, t, is equal to zero. Substituting t = 0 into the equation h = -16t^2 + 16t + 50, we get:
h = -16(0)^2 + 16(0) + 50
h = 0 + 0 + 50
h = 50
Therefore, the height of the ramp is 50 feet.
To find the maximum height achieved, we need to find the vertex of the quadratic equation h = -16t^2 + 16t + 50. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where the equation is in the form ax^2 + bx + c = 0. In this case, a = -16 and b = 16.
t = -16/(2 * -16)
t = -16/(-32)
t = 0.5
Substituting t = 0.5 into the equation h = -16t^2 + 16t + 50, we get:
h = -16(0.5)^2 + 16(0.5) + 50
h = -16(0.25) + 8 + 50
h = -4 + 8 + 50
h = 54
Therefore, the maximum height achieved is 54 feet.
h = -16(0)^2 + 16(0) + 50
h = 0 + 0 + 50
h = 50
Therefore, the height of the ramp is 50 feet.
To find the maximum height achieved, we need to find the vertex of the quadratic equation h = -16t^2 + 16t + 50. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where the equation is in the form ax^2 + bx + c = 0. In this case, a = -16 and b = 16.
t = -16/(2 * -16)
t = -16/(-32)
t = 0.5
Substituting t = 0.5 into the equation h = -16t^2 + 16t + 50, we get:
h = -16(0.5)^2 + 16(0.5) + 50
h = -16(0.25) + 8 + 50
h = -4 + 8 + 50
h = 54
Therefore, the maximum height achieved is 54 feet.
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