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.
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?
1 answer
2 answers