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?
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.
To find the height of the ramp, we need to determine the initial height when the car first took off. In the given equation, h = -16t^2 + 16t + 50, the term "50" represents the initial height, which is the height of the ramp.
Therefore, the height of the ramp is 50 feet.
To find the maximum height achieved by the car, we need to locate the vertex of the parabolic equation. The vertex represents the maximum or minimum point of the graph.
The equation for the height is in the form h = at^2 + bt + c, where a = -16, b = 16, and c = 50.
The x-coordinate of the vertex, or t-value, can be determined using the formula t = -b / (2a).
Substituting the values of a and b into the formula, we get t = -16 / (2 * -16) = -16 / -32 = 0.5 seconds.
To find the maximum height, substitute the t-value back into the original equation for h.
h = -16(0.5)^2 + 16(0.5) + 50
h = -16(0.25) + 8 + 50
h = -4 + 8 + 50
h = 54 feet
Therefore, the maximum height achieved by the car is 54 feet.
To find the height of the ramp, we need to determine the initial height h(0) when t = 0 seconds.
Given the equation h(t) = -16t^2 + 16t + 50, we substitute t = 0 to find h(0):
h(0) = -16(0)^2 + 16(0) + 50
= 0 + 0 + 50
= 50 feet
Therefore, the height of the ramp is 50 feet.
To find the maximum height achieved, we can determine the vertex of the parabolic equation h(t) = -16t^2 + 16t + 50. The vertex represents the highest point of the parabola.
The x-coordinate of the vertex is given by the formula t = -b / (2a), where a, b, and c are the coefficients in the equation h(t) = at^2 + bt + c.
In this case, a = -16 and b = 16. Let's calculate the x-coordinate of the vertex:
t = -16 / (2(-16))
= -16 / (-32)
= 0.5 seconds
Now, substitute this value back into the equation h(t) to find the maximum height:
h(0.5) = -16(0.5)^2 + 16(0.5) + 50
= -16(0.25) + 8 + 50
= -4 + 8 + 50
= 54 feet
Therefore, the maximum height achieved by the stunt driver is 54 feet.